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To explore how rigid rotation affects the thermodynamic properties of free relativistic bosons, we employ the standard imaginary time formalism of thermal field theory to calculate the free propagator of complex scalar fields under rotation. We introduce the corresponding partition function and explicitly compute it by expanding the modes in cylindrical coordinates. The resulting propagator is in full agreement with similar findings in the existing literature., Comment: 4 pages, talk presented by E. Siri at the 8th Iranian Conference on Mathematical Physics (ICMP) in Qom, Iran, on 7-8 July 2024; Submitted to Transactions in Theoretical and Mathematical Physics (TTMP)

We study the thermodynamic properties of a rigidly rotating relativistic Bose gas. First, we derive the solution of the equation of motion corresponding to a rotating complex Klein-Gordon field and determine the free propagator of this model utilizing the Fock-Schwinger proper-time method. Using this propagator, we then obtain the thermodynamic potential of this model in the zeroth and first perturbative level. In addition, we compute the nonperturbative ring contribution to this potential. Our focus is on the dependence of these expressions on the angular velocity, which effectively acts as a chemical potential. Using this thermodynamic potential, we calculate several quantities, including the pressure, angular momentum and entropy densities, heat capacity, speed of sound, and moment of inertia of this rigidly rotating Bose gas as functions of temperature ($T$), angular velocity ($\Omega$), and the coupling constant ($\alpha$). We show that certain thermodynamic instabilities appear at high temperatures and large couplings. They are manifested as zero and negative values of the above quantities, particularly the moment of inertia and heat capacity. Zero moment of inertia leads to the phenomenon of supervorticity at certain $T$ or $\alpha$. Supervortical temperatures (couplings) decrease with increasing coupling (temperature). We also observe superluminal sound velocities at high $T$ and for large $\alpha$., Comment: V1: 25 pages, 20 figures; V2: Typos corrected, References updated, accepted for publication in PRD

We generalize a recently introduced formulation of relativistic spinful and vortical fluid to relativistic magnetohydrodynamics (MHD). We refer to it as the "Spinful-Vortical MHD" (SVMHD). The aim is to scrutinize the interplay between the vorticity, magnetic field, and spin, which is treated as a quantum object, in contrast to other formulations of spin hydrodynamics. To this purpose, we first perform a standard entropy current analysis up to first-order gradient expansion, $\mathcal{O}\left(\partial\right)$ as well as $\mathcal{O}\left(\hbar\partial\right)$, where $\hbar$ is the Planck constant. In contrast to alternative formulations of spin MHD, in the absence of vorticity, the zeroth-order energy-momentum tensor includes an additional magneto-vorticity mixed term and reduces, as expected, to the energy-momentum tensor of MHD. We show that in the first-order of gradient expansion, $36$ dissipative transport coefficients appear. They satisfy certain constraints that guarantee the positive definiteness of the entropy production rate. We then modify the formulation of SVMHD by replacing the magnetic part of the thermal vorticity tensor with its electric part. Carrying out the same analysis as in the standard formulation, we show that in this case, the first-order constitutive relations consist of $11$ nondissipative Hall-like coefficients, apart from $25$ dissipative coefficients. This difference arises from different behavior of the electric and magnetic part of the thermal vorticity under time-reversal transformation., Comment: 13 pages

The effect of rotation on the formation of the magnetic dual chiral density wave (\MD) in a dense and magnetized cold quark matter is studied. This phase is supposed to exist in the extreme conditions prevailing, e.g., in a neutron star. These conditions are, apart from high densities and strong magnetic fields, a relatively large angular velocity. To answer the question of whether the rotation enhances or suppresses the formation of this phase, we first determine the effect of rotation on the energy dispersion relation of a fermionic system in the presence of a constant magnetic field and then focus on the thermodynamic potential of the model at low temperature $T$ and finite chemical potential $\mu$. The thermodynamic potential consists, in particular, of an anomalous part leading to certain topological effects. We show that in comparison with the nonrotating case, a term proportional to the angular velocity appears in this anomalous potential. We then solve the corresponding gap equations to the chiral and spatial modulation condensates, and study the dependence of these dynamical variables on the chemical potential ($\mu$), magnetic field ($eB$), and angular velocity ($\Omega$). It turns out that the interplay between these parameters suppresses the formation of the \MD~phase in relevant regimes for cold neutron stars. This is interpreted as the manifestation of the inverse magnetorotational catalysis, which is also reflected in the phase portraits $eB$-$\mu$, $eB$-$\Omega R$, and $\mu$-$\Omega R$, explored in this work., Comment: V1: 19 pages, 7 figures, 2 tables; V2: Discussions improved, accepted for publication in PRD

We study the properties of a hot and magnetized quark matter in a rotating cylinder in the presence of a constant magnetic field. To do this, we solve the corresponding Dirac equation using the Ritus eigenfunction method. This leads to the energy dispersion relation, Ritus eigenfunctions, and the quantization relation for magnetized fermions. To avoid causality-violating effects, we impose a certain global boundary condition, and study its effect, in particular, on the energy eigenmodes and the quantization relations of fermions. Using the fermion propagator arising from this method, we then solve the gap equation at zero and nonzero temperatures. At zero temperature, the dynamical mass $\bar{m}$ does not depend on the angular frequency, as expected. We thus study its dependence on the distance $r$ relative to the axis of rotation and the magnetic field $B$, and explore the corresponding finite size effect for various couplings $G$. We then consider the finite temperature case. The dependence of $\bar{m}$ on the temperature $T$, magnetic field $B$, angular frequency $\Omega$, and distance $r$ for various $G$ is studied. We show that $\bar{m}$ decreases, in general, with $B$ and $\Omega$. This is the ''inverse magneto-rotational catalysis (IMRC)'' or the ''rotational magnetic inhibition'', previously discussed in the literature. To explore the evidence of this effect in the phase diagrams of our model, we examine the phase portraits of the critical temperature $T_c$ as well as the critical angular frequency $\Omega_c$ with respect to $G, B,\Omega$, and $r$ as well as $G, B, T$, and $r$, respectively. We show that $T_{c}$ and $\Omega_c$ decrease, in particular, with $B$. This is interpreted as clear evidence for IMRC., Comment: 23 pages, 12 figures, 5 tables

The Chern-Simons magnetohydrodynamics (CSMHD) is introduced using a Maxwell-Chern-Simons (MCS) Lagrangian including an axion-like field $\Theta$. The MCS equation of motion derived from this Lagrangian consists of a modified current, including a chiral magnetic (CM) and an anomalous Hall (AH) current, in addition to the ordinary Ohm current of resistive magnetohydrodynamics (MHD). The former consists of an axial chemical potential, which is given in terms of the temporal comoving derivative of $\Theta$, and the latter arises from the spatial gradient of $\Theta$. As it turns out, the existence of the axial chemical potential is a nonequilibrium effect that plays no role in the linear stability analysis, whereas the AH current arises as in the first-order linear perturbation of the thermal equilibrium. We analyze the linear stability and causality of the CSMHD in a resistive and chiral medium. We show that the Alfven modes propagating sufficiently close to the direction of the magnetic field are unstable but causal. They are also accompanied by a genuine nonhydro mode. A stable mode in a particular direction can correspond to an unstable mode propagating in the exact opposite direction. The AH instability is a manifestation of a breakdown of the parity. A numerical analysis of the phase velocity confirms these results., Comment: 31 pages, 10 figures

By combining the Wigner function formalism of relativistic quantum kinetic theory with fundamental equations of relativistic magnetohydrodynamics (MHD), we present a novel approach to determine the proper time evolution of the temperature and other thermodynamic quantities in a uniformly expanding hot, magnetized, and weakly interacting plasma. The aim is to study the contribution of quantum corrections to this evolution. We first determine the corresponding Wigner function in terms of the solution of the Dirac equation in the presence of a constant magnetic field. Using this function, we then compute the energy-momentum tensor of the above-mentioned plasma, which eventually yields its energy density and pressure. Plugging these quantities in the energy equation of relativistic MHD, we arrive, after choosing an appropriate coordinate system, at a differential equation for the temperature as a function of the proper time. The numerical solution of this equation leads finally to the proper time evolution of the temperature. The latter is then used to determine the evolution of a large number of thermodynamic quantities in this expanding and magnetized plasma. We compare our results with other existing results from relativistic MHD. We also comment on the effect of point to point decaying magnetic fields on the thermodynamic properties of this plasma., Comment: 23 pages, 9 figures

In ultrarelativistic heavy-ion collisions, enormous magnetic fields are generated because of fast-moving charged particles. In the presence of these magnetic fields, the spin of particles is aligned either in the parallel or in the antiparallel direction with respect to the direction of the magnetic field. A finite magnetization is thus produced. It is known that a finite magnetic susceptibility, $\chi_{m}$, changes the evolution of the energy density of the quark-gluon plasma (QGP), which is believed to be created in these collisions. Depending on whether the system under consideration is a paramagnetic ($\chi_{m}>0$) or diamagnetic ($\chi_{m}<0$) fluid, it slows down or speeds up the decay of the energy density, and affects other thermodynamic quantities. In general, one expects that the magnetic susceptibility depends on the magnetic field and temperature. Bearing in mind that these parameters evolve with the evolution of the fluid, a nonuniform magnetic susceptibility in this system is thus expected. In this work, we first determine $\chi_{m}$ by using a certain analogy to the standard anisotropic kinetic theory, where the one-particle distribution function is replaced by the corresponding anisotropic distribution function. We then determine the proper time dependence of the magnetic susceptibility in the framework of the ideal transverse magnetohydrodynamics. We also study the effect of dissipation on the evolution of $\chi_{m}$., Comment: 8 pages, 4 figures, XIII Quark Confinement and the Hadron Spectrum - Confinement2018, 31 July - 6 August 2018, Maynooth University, Ireland

Due to the absence of a transverse expansion with respect to the beam direction, the Bjorken flow is unable to describe certain observables in heavy ion collisions. This caveat has motivated the introduction of analytical relativistic hydrodynamics (RH) solutions with transverse expansion, in particular, the 3+1 self-similar (SSF) and Gubser flows. Inspired by recent generalizations of the Bjorken flow to the relativistic magnetohydrodynamics (RMHD), we present a procedure for a generalization of RH solutions to RMHD. Our method is mainly based on symmetry arguments. Using this method, we find the relation between RH degrees of freedom and the magnetic field evolution in the ideal limit for an infinitely conductive fluid, and determine the proper time dependence of the magnetic field in aforementioned flows. In the case of SSF, a family of solutions are found that are related through a certain differential equation. To find the magnetic field evolution in the Gubser flow, we solve RMHD equations for a stationary fluid in a conformally flat $dS^3\times E^1$ spacetime. The result is then Weyl transformed back into the Minkowski spacetime. In this case, the temporal evolution of the magnetic field exhibits a transmission between $1/t$ to $1/t^3$ near the center of the collision. The longitudinal component of the magnetic field is found to be sensitive to the transverse size of the fluid. We also find the radial evolution of the magnetic field for both flows. The radial domain of validity in the case of SSF is highly restricted, in contrast to the Gubser flow. A comparison of the results suggests that the Gubser RMHD may give a more appropriate qualitative picture of the magnetic field decay in the quark-gluon plasma (QGP)., Comment: 8 pages, 1 figures, XIII Quark Confinement and the Hadron Spectrum - Confinement2018, 31 July - 6 August 2018, Maynooth University, Ireland

The plasma of quarks and gluons created in ultrarelativistic heavy-ion collisions turns out to be paramagnetic. In the presence of a background magnetic field, this paramagnetism thus leads to a pressure anisotropy, similar to anisotropies appearing in a viscous fluid. In the present paper, we use this analogy, and develop a framework similar to anisotropic hydrodynamics, to take the pressure anisotropy caused, in particular, by the nonvanishing magnetization of a plasma of quarks and gluons into account. We consider the first two moments of the classical Boltzmann equation in the presence of an electromagnetic source in the relaxation-time approximation, and derive a set of coupled differential equations for the anisotropy parameter $\xi_0$ and the effective temperature $\lambda_0$ of an ideal fluid with nonvanishing magnetization. We also extend this method to a dissipative fluid with finite magnetization in the presence of a strong and dynamical magnetic field. We present a systematic method leading to the one-particle distribution function of this magnetized dissipative medium in a first-order derivative expansion, and arrive at analytical expressions for the shear and bulk viscosities in terms of the anisotropy parameter $\xi$ and effective temperature $\lambda$. We then solve the corresponding differential equations for $(\xi_0,\lambda_0)$ and $(\xi,\lambda)$ numerically, and determine, in this way, the proper time and temperature dependence of the energy density, directional pressures, speed of sound, and the magnetic susceptibility of a longitudinally expanding magnetized quark-gluon plasma in and out of equilibrium., Comment: V1:23 pages, 16 figures; V2: Typos corrected, version accepted for publication in PRD (2019)

Motivated by the recently found realization of the $1+1$ dimensional Bjorken flow in ideal and nonideal relativistic magnetohydrodynamics (MHD), we use appropriate symmetry arguments, and determine the evolution of magnetic fields arising from the $3+1$ dimensional self-similar and Gubser flows in an infinitely conductive relativistic fluid (ideal MHD). In the case of the $3+1$ dimensional self-similar flow, we arrive at a family of solutions, that are related through a differential equation arising from the corresponding Euler equation. To find the magnetic field evolution from the Gubser flow, we solve the MHD equations of a stationary fluid in a conformally flat $dS^{3}\times E^{1}$ spacetime. The results are then Weyl transformed back into the Minkowski spacetime. In this case, the temporal evolution of the resulting magnetic field is shown to exhibit a transition between an early time $1/t$ decay to a $1/t^{3}$ decay at a late time. Here, $t$ is the time coordinate. Transverse and longitudinal components of the magnetic fields arising from these flows are also found. The latter turns out to be sensitive to the transverse size of the fluid. In contrast to the result arising from the Gubser flow, the radial domain of validity of the magnetic field arising from the self-similar flow is highly restricted. A comparison of the results suggests that the (conformal) Gubser MHD may give a more appropriate qualitative picture of the magnetic field decay in the plasma of quarks and gluons created in heavy ion collisions., Comment: 26 pages, 10 figures

In order to gain deeper insight into the physics of the novel rotating solution of nonideal transverse magnetohydrodynamics (MHD), presented in one of our recent works, we replace the previously considered Maxwell theory with the ${\cal{CP}}$ violating Maxwell-Chern-Simons (MCS) theory. In this way, dissipationless chiral magnetic (CM) and anomalous Hall (AH) currents appear in the MCS equation of motion, that, together with equations of relativistic hydrodynamics, builds the set of constitutive equations of the nonideal transverse Chern-Simons magnetohydrodynamics (CSMHD). We are, in particular, interested in the effect of these currents on the evolution of electromagnetic fields in a uniformly and longitudinally expanding quark-gluon plasma with chirality imbalance. Combining the constitutive equations of CSMHD under these assumptions, we arrive, as expected, at two distinct rotating and nonrotating solutions for electromagnetic fields. The rotation occurs with increasing rapidity and a constant angular velocity $\omega_{0}$. Remarkably, the relative angle between the electric and magnetic fields, $\delta$, turns out to be given by the coefficient of AH current $\kappa_{E}$ and the electric conductivity of the medium $\sigma$, as $\delta=\tan^{-1}(\kappa_{E}/\sigma)$. Whereas the nonrotating solution implies the AH coefficient to be vanishing, and thus nonrotating electric and magnetic fields to be either parallel or antiparallel, the relative orientation of rotating electric and magnetic fields and the evolution of the CM conductivity $\kappa_{B}$ are strongly affected by nonvanishing $\kappa_{E}$. We explore the effect of positive and negative $\omega_{0}$ on the evolution of the CM current, and show, in particular, that a rotation of electromagnetic fields with negative $\omega_{0}$ implies a sign flip of the CM current in a chiral fluid with nonvanishing AH current., Comment: V1: 25 pages, 15 figures, 1 table; V2: Discussions improved. Version accepted for publication in PRD

The evolution of electromagnetic and thermodynamic fields in a non-ideal fluid are studied in the framework of ultrarelativistic transverse magnetohydrodynamics (MHD), which is essentially characterized by electric and magnetic fields being transverse to the fluid velocity. Extending the method of self-similar solutions of relativistic hydrodynamics to the case of non-conserved charges, the differential equations of non-ideal transverse MHD are solved, and two novel sets of self-similar solutions are derived. The first set turns out to be a boost-invariant and exact solution, which is characterized by non-rotating electric and magnetic fields. The second set is a non-boost-invariant solution, which is characterized by rotating electric and magnetic fields. The rotation occurs with increasing rapidity $\eta$, as the angular velocity is defined by $\omega_{0}\equiv\frac{\partial\zeta}{\partial\eta}=\frac{\partial\phi}{\partial\eta}$, with $\zeta$ and $\phi$ being the angles of electric and magnetic vectors with respect to a certain axis in the local rest frame of the fluid. For both sets of solutions, the electric and magnetic fields are either parallel or anti-parallel to each other. Performing a complete numerical analysis, the effects of finite electric conductivity as well as electric and magnetic susceptibilities of the medium on the evolution of rotating and non-rotating MHD solutions are explored, and the interplay between the angular velocity $\omega_{0}$ and these quantities is scrutinized. The lifetime of electromagnetic fields and the evolution of the temperature of the electromagnetized fluid are shown to be affected by $\omega_{0}$., Comment: 33 pages, 18 figures

The effects of finite magnetization and electric polarization on dissipative and non-dissipative (anomalous) transport coefficients of a chiral fluid are studied. First, using the second law of thermodynamics as well as Onsager's time reversal symmetry principle, the complete set of dissipative transport coefficients of this medium is derived. It is shown that the properties of the resulting shear and bulk viscosities are mainly affected by the anisotropy induced by external electric and magnetic fields. Then, using the fact that the anomaly induced currents do not contribute to entropy production, the corresponding algebro-differential equations to non-dissipative anomalous transport coefficients are derived in a certain derivative expansion. The solutions of these equations show that, within this approximation, anomalous transport coefficients are, in particular, given in terms of the electric susceptibility of the medium., Comment: V1: 14 pages (two-column), 1 table, no figure; V2: 20 pages (one-column), 1 table, no figure. Version accepted for publication in New Journal of Physics (2017)

The differential multiplicity of dileptons in a hot and magnetized quark-gluon plasma, $\Delta_{B}\equiv dN_{B}/d^{4}xd^{4}q$, is derived from first principles. The constant magnetic field $B$ is assumed to be aligned in a fixed spatial direction. It is shown that the anisotropy induced by the $B$ field is mainly reflected in the general structure of photon spectral density function. This is related to the imaginary part of the vacuum polarization tensor, $\mbox{Im}[\Pi^{\mu\nu}]$, which is derived in a first order perturbative approximation. As expected, the final analytical expression for $\Delta_{B}$ includes a trace over the product of a photonic part, $\mbox{Im}[\Pi^{\mu\nu}]$, and a leptonic part, ${\cal{L}}_{\mu\nu}$. It is shown that $\Delta_{B}$ consists of two parts, $\Delta_{B}^{\|}$ and $\Delta_{B}^{\perp}$, arising from the components $(\mu,\nu)=(\|,\|)$ and $(\mu,\nu)=(\perp,\perp)$ of $\mbox{Im}[\Pi^{\mu\nu}]$ and ${\cal{L}}_{\mu\nu}$. Here, the transverse and longitudinal directions are defined with respect to the direction of the $B$ field. Combining $\Delta_{B}^{\|}$ and $\Delta_{B}^{\perp}$, a novel anisotropy factor $\nu_{B}$ is introduced. Using the final analytical expression of $\Delta_{B}$, the possible interplay between the temperature $T$ and the magnetic field strength $eB$ on the ratio $\Delta_{B}/\Delta_{0}$ and $\nu_{B}$ is numerically studied. Here, $\Delta_{0}$ is the Born approximated dilepton multiplicity in the absence of external magnetic fields. It is, in particular, shown that for each fixed $T$ and $B$, in the vicinity of certain threshold energies, $\Delta_{B}\gg \Delta_{0}$ and $\Delta_{B}^{\perp}\gg \Delta_{B}^{\|}$. The latter anisotropy may be interpreted as one of the microscopic sources of the macroscopic anisotropies, reflecting themselves, e.g., in the elliptic asymmetry factor $v_{2}$ of dileptons., Comment: V1: 24 pages (two-column), 11 figures, 1 table; V2: 44 pages (one-column), 12 figures, 2 tables. Typos corrected, discussions improved, references updated, appendix B added; V3: 41 pages (one-column), 12 figures, 2 tables, discussions improved. Version accepted for publication in AOP (2017)

Using the standard Green-Kubo formalism, we determine the shear viscosity $\eta$ of a hot and dense Yukawa-Fermi gas. In particular, we study the effect of particle and plasmino excitations on thermal properties of the fermionic part of the shear viscosity, and explore the effects of thermal corrections to particle masses on bosonic and fermionic shear viscosities, $\eta_b$ and $\eta_f$. It turns out that the effects of plasminos on $\eta_f$ become negligible with increasing (decreasing) temperature (chemical potential)., Comment: 8 pages, 7 figures, Poster presented by F. Taghinavaz at "XIth Quark Confinement and the Hadron Spectrum", Saint-Petersburg, Russia, 8-12 September 2014

The complete quasi-particle spectrum of a magnetized electromagnetic plasma is systematically explored at zero and nonzero temperatures. To this purpose, the general structure of the one-loop corrected propagator of magnetized fermions is determined, and the dispersion relations arising from the pole of this propagator are numerically solved. It turns out that in the lowest Landau level, where only one spin direction is allowed, the spectrum consists of one positively (negatively) charged fermionic mode with positive (negative) spin. In contrast, in higher Landau levels, as an indirect consequence of the double spin degeneracy of fermions, the spectrum consists of two massless collective modes with left- and right-chiralities. The mechanism through which these new collective excitations are created in a uniform magnetic field is similar to the production mechanism of dynamical holes (plasminos) at finite temperature and zero magnetic fields. Whereas cold magnetized plasminos appear for moderate magnetic fields and for all positive momenta of propagating fermions, hot magnetized plasminos appear only in the limit of weak magnetic fields and soft momenta., Comment: V1: 24 pages, 10 figures; V2: Typos corrected. Version accepted for publication in PRD

The effect of anomalous magnetic moment of quarks on thermodynamic properties of the chiral condensate is studied, using of a two-flavor Nambu--Jona-Lasinio model at finite temperature $T$, chemical potential $\mu$, and in the presence of a uniform magnetic field $eB$. To this purpose, the Schwinger linear-in-$B$ ansatz for the quark anomalous magnetic moment in term of the nonperturbative Bohr magneton is considered. In a two-dimensional flavor space, it leads to the correction $\hat{T}_{Sch}=\hat{\kappa}\hat{Q} eB$ in the energy dispersion relation of quarks. Here, $\hat{Q}$ is the quark charge matrix. We consider three different sets for $\hat{\kappa}$, and numerically determine the dependence of the constituent quark mass on $T,\mu$ and $eB$ for fixed $\hat{\kappa}$. By exploring the complete phase portrait of this model in $T$-$\mu$, $\mu$-$eB$, and $T$-$eB$ phase spaces for various fixed $eB$, $T$, $\mu$ and $\hat{\kappa}$, we observe that inverse magnetic catalysis occurs for large enough $\hat{\kappa}$. Moreover, in the regime of weak magnetic fields, the phenomenon of reentrance of chiral symmetry broken and restored phases occurs for $T, \mu$ and $eB$ dependent $\hat{\kappa}$., Comment: 22 pages, 14 figures

We determine the shear viscosity of a hot and dense Yukawa-Fermi gas, using the standard Green-Kubo relation, according to which the shear viscosity is given by the retarded correlator of the traceless part of viscous energy-momentum tensor. We approximate this retarded correlator using a one-loop skeleton expansion, and express the bosonic and fermionic shear viscosities, $\eta_{b}$ and $\eta_{f}$, in terms of bosonic and fermionic spectral widths, $\Gamma_{b}$ and $\Gamma_{\pm}$. Here, the subscripts $\pm$ correspond to normal and collective (plasmino) excitations of fermions. We study, in particular, the effect of these excitations on thermal properties of $\eta_{f}[\Gamma_{\pm}]$. To do this, we determine first the dependence of $\Gamma_{b}$ and $\Gamma_{\pm}$ on momentum $p$, temperature $T$, chemical potential $\mu$ and $\xi_{0}\equiv m_{b}^{0}/m_{f}^{0}$, in a one-loop perturbative expansion in the orders of the Yukawa coupling. Here, $m_{b}^{0}$ and $m_{f}^{0}$ are $T$ and $\mu$ independent bosonic and fermionic masses, respectively. We then numerically determine $\eta_{b}[\Gamma_{b}]$ and $\eta_{f}[\Gamma_{\pm}]$, and study their thermal properties. It turns out that whereas $\Gamma_{b}$ and $\Gamma_{+}$ decrease with increasing $T$ or $\mu$, $\Gamma_{-}$ increases with increasing $T$ or $\mu$. This behavior qualitatively changes by adding thermal corrections to $m_{b}^{0}$ and $m_{f}^{0}$, while the difference between $\Gamma_{+}$ and $\Gamma_{-}$ keeps increasing with increasing $T$ or $\mu$. Moreover, $\eta_{b}$ ($\eta_{f}$) increases (decreases) with increasing $T$ or $\mu$. We show that the effect of plasminos on $\eta_{f}$ becomes negligible with increasing (decreasing) $T$ ($\mu$)., Comment: V1: 25 pages, 18 figures; V2: 26 pages, 18 figures. Discussions improved, references added. Version accepted for publication in PRD

The directional weak decay constants of neutral pions are determined at finite temperature T, chemical potential \mu and in the presence of a constant magnetic field B. To do this, we first derive the energy dispersion relation of neutral pions from the corresponding effective action of a two-flavor, hot and magnetized Nambu--Jona-Lasinio model. Using this dispersion relation, including nontrivial directional refraction indices, we then generalize the PCAC relation of neutral pions and derive the Goldberger-Treiman (GT) as well as the Gell--Mann-Oakes-Renner (GOR) relations consisting of directional quark-pion coupling constant g_{qq\pi^{0}}^{(\mu)} and weak decay constant f_{\pi^{0}}^{(\mu)} of neutral pions. The temperature dependence of g_{qq\pi^{0}}^{(\mu)} and f_{\pi^{0}}^{(\mu)}, are then determined for fixed chemical potential and various constant background magnetic fields. The GT and GOR relations are also verified at finite T,\mu and eB. It is shown that, because of the explicit breaking of the Lorentz invariance by the magnetic field, the directional quark-pion coupling and decay constants of neutral pions in the longitudinal and transverse directions with respect to the direction of the external magnetic field are different, i.e. g_{qq\pi^{0}}^{\|}\neq g_{qq\pi^{0}}^{\perp} and f_{\pi^{0}}^{\|}\neq f_{\pi^{0}}^{\perp}. As it turns out, for fixed T,\mu and B, g_{qq\pi^{0}}^{\|}> g_{qq\pi^{0}}^{\perp} and f_{\pi^{0}}^{\|}< f_{\pi^{0}}^{\perp}., Comment: V1: 25 pages, 15 figures; V2: 27 pages, 15 figures, 1 table. Discussions improved, references updated. Version accepted for publication in PRD

Utilizing an extended two-flavor Nambu-Jona Lasinio (NJL) model, we review some of the effects of external magnetic fields on two-flavor color superconducting phase (2SC) at moderate baryon densities in the QCD phase diagram. The effective action of the extended NJL model consists of two mass gaps as functions of three intensive quantities, the temperature, the quark chemical potential and the external magnetic field. The nonzero values of the mass gaps, chiral and diquark condensates, induce spontaneous chiral and color symmetry breaking, respectively, and as a result two different phases of quark matter appear. We find the transition curves between these phases as well as the critical points in the QCD phase diagram in terms of the intensive quantities. Imposing a constant strong magnetic field on these two phases, we show that the mass gaps increase with the magnetic field and the symmetry breaking region in the QCD phase diagram expands even to the larger values of temperature and quark chemical potential. This phenomenon is a consequence of the magnetic catalysis of dynamical symmetry breaking, which is proven before.

The properties of non-interacting $\sigma$ and $\pi^{0}$ mesons are studied at finite temperature, chemical potential and in the presence of a constant magnetic field. To do this, the energy dispersion relations of these particles, including nontrivial form factors, are derived using a derivative expansion of the effective action of a two-flavor, hot and magnetized Nambu--Jona-Lasinio (NJL) model up to second order. The temperature dependence of the pole and screening masses as well as the directional refraction indices of magnetized neutral mesons are explored for fixed magnetic fields and chemical potentials. It is shown that, because of the explicit breaking of the Lorentz invariance by the magnetic field, the refraction index and the screening mass of neutral mesons exhibit a certain anisotropy in the transverse and longitudinal directions with respect to the direction of the external magnetic field. In contrast to their longitudinal refraction indices, the transverse indices of the neutral mesons are larger than unity., Comment: V1: 26 pages, 15 figures; V2: Discussions improved, references added. Version accepted for publication in PRD

The effect of an exponentially decaying magnetic field on the dynamics of Dirac fermions in 3+1 dimensions is explored. The spatially decaying magnetic field is assumed to be aligned in the third direction, and is defined by {\mathbf{B}}(x)=B(x){\mathbf{e}}_{z}, with B(x)=B_{0}e^{-\xi\ x/\ell_{B}}. Here, \xi\ is a dimensionless damping factor and \ell_{B}=(eB_{0})^{-1/2} is the magnetic length. As it turns out, the energy spectrum of fermions in this inhomogeneous magnetic field can be analytically determined using the Ritus method. Assuming the magnetic field to be strong, the chiral condensate and the \textit{local} electric current correlation function are computed in the lowest Landau level (LLL) approximation and the results are compared with those arising from a strong homogeneous magnetic field. Although the constant magnetic field B_{0} can be reproduced by taking the limit of \xi-> 0 and/or x-> 0 from B(x), these limits turn out to be singular once the quantum corrections are taken into account., Comment: V1: 16 pages, 7 figures, 2 tables; V2: Section II improved, references added. Version accepted for publication in PRD

A hidden generalized gauge symmetry of a cutoff QED is used to show the renormalizability of QED. In particular, it is shown that corresponding Ward identities are valid all along the renormalization group flow. The exact Renormalization Group flow equation corresponding to the effective action of a cutoff lambda phi^4 theory is also derived. Generalization to any gauge group is indicated., Comment: V1: 18 pages, 2 figures; V2: Discussions improved. Version accepted for publication in Physica Scripta

The mass spectrum of the noncommutative QED in two-dimensional Euclidean $\mathbb{R}^{2}$ space is derived first in a perturbative approach at one-loop level and then in a nonperturbative approach using the equivalent bosonized noncommutative effective action. It turns out that the mass spectrum of noncommutative QED in two dimensions reduces to a single non-interacting meson with mass $M_{\gamma}=\frac{g}{\sqrt{\pi}}$, as in commutative Schwinger model., Comment: 23 pages, 2 figures; V2: References added. The first paragraph of the Introduction revised. Version accepted for publication in EPJC

A two-flavor color superconducting (2SC) Nambu--Jona-Lasinio (NJL) model is introduced at finite temperature T, chemical potential mu and in the presence of a constant magnetic field eB. The effect of (T,mu,eB) on the formation of chiral and color symmetry breaking condensates is studied. The complete phase portrait of the model in T-mu, mu-eB, and T-eB phase spaces for various fixed eB, T, and mu is explored. A threshold magnetic field eB_t~ 0.5 GeV^2 is found above which the dynamics of the system is solely dominated by the lowest Landau level (LLL) and the effects of T and mu are partly compensated by eB., Comment: V1: 29 pages, 15 figures, 3 tables. V2: Discussions improved. Version accepted for publication in PRD

A generalized translational invariant noncommutative field theory is analyzed in detail, and a complete description of translational invariant noncommutative structures is worked out. The relevant gauge theory is described, and the planar and nonplanar axial anomalies are obtained., Comment: V1: 23 pages, 4 figures; V2: Section I. improved, References added. Version accepted for publication in PRD

The color neutral two-flavor superconducting (2SC) phase of cold and dense quark matter is studied in the presence of constant magnetic fields and at moderate baryon densities. In the first part of the paper, a two-flavor effective Nambu--Jona-Lasinio model consisting of a chiral symmetry breaking mass gap sigma_{B}, a color superconducting mass gap Delta_{B} and a color neutrality coefficient mu_{8} is introduced in the presence of a rotated U(1) magnetic field B. To study the phenomenon of magnetic catalysis in the presence of strong magnetic fields, the gap equations corresponding to sigma_{B} and Delta_{B}, as well as mu_{8} are solved in the lowest Landau level approximation. In the second part of the paper, a detailed numerical analysis is performed to explore the effect of any arbitrary magnetic field on the above mass gaps and the color neutrality coefficient. The structure of the chiral symmetry breaking and color superconducting phases is also presented in the mu_{c}-B plane, and the effect of the color neutrality coefficient mu_{8} on the phase structure of the model is explored. As it turns out, whereas the transition from the chiral symmetry breaking to color superconducting phase is of first order, nonvanishing mu_{8} affects essentially the second order phase transition from color superconducting to the normal phase., Comment: 33 pages, 9 Figures, 5 Tables; V2: Version accepted for publication in PRD

Using the method of perturbative quantization in the first order approximation, we quantize a non-local QED-like theory including fermions and bosons whose interactions are described by terms containing higher order space-time derivatives. As an example, the two-dimensional space-time noncommutative QED (NC-QED) is quantized perturbatively up to O(e^2,\theta^3), where e is the NC-QED coupling constant and \theta is the noncommutativity parameter. The resulting modified Lagrangian density is shown to include terms consisting of first order time-derivative and higher order space-derivatives of the modified field variables that satisfy the ordinary equal-time commutation relations up to O(e^2,\theta^3. Using these commutation relations, the canonical current algebra of the modified theory is also derived., Comment: 22 pages, no figures

To study the effect of a strong magnetic field $B$ on the sound velocity $v_{s}$ of plane waves propagating in a strongly magnetized quark-gluon plasma (QGP), a chiral magnetohydrodynamical (MHD) description of a perfect (non-dissipative) QGP exhibiting dynamical chiral symmetry breaking (D$\chi$SB) is developed using the effective action of the Nambu-Jona-Lasinio (NJL) model of QCD at finite temperature, finite baryon chemical potential and in the presence of a strong magnetic field. Here, the D$\chi$SB arises due to the phenomenon of magnetic catalysis. Apart from an interesting frequency dependence, for plane waves propagating in the transverse or longitudinal direction with respect to the $B$ field, the sound velocity is anisotropic and depends on the angle between the corresponding wave vectors and the direction of the $B$ field. Moreover, for plane waves propagating in the transverse (longitudinal) direction to the external $B$ field, the sound velocity has a maximum (minimum) at $T

Using the general structure of the vacuum polarization tensor $\Pi_{\mu\nu}(k_{0},\mathbf{k})$ in the infrared (IR) limit, $k_{0}\to 0$, the ring contribution to QED effective potential at finite temperature and non-zero magnetic field is determined beyond the static limit, $(k_{0}\to 0,\mathbf{k}\to \mathbf{0})$. The resulting ring potential is then studied in weak and strong magnetic field limit. In the limit of weak magnetic field, at high temperature and for $\alpha\to 0$, the improved ring potential consists of a term proportional to $T^{4}\alpha^{5/2}$, in addition to the expected $T^{4}\alpha^{3/2}$ term arising from the static limit. Here, $\alpha$ is the fine structure constant. In the limit of strong magnetic field, where QED dynamics is dominated by the lowest Landau level (LLL), the ring potential includes a novel term consisting of dilogarithmic function $(eB){Li}_{2}(-\frac{2\alpha}{\pi}\frac{eB}{m^{2}})$. Using the ring improved (one-loop) effective potential including the one-loop effective potential and ring potential in the IR limit, the dynamical chiral symmetry breaking of QED is studied at finite temperature and in the presence of strong magnetic field. The gap equation, the dynamical mass and the critical temperature of QED in the regime of LLL dominance are determined in the improved IR as well as in the static limit. For a given value of magnetic field, the improved ring potential is shown to be more efficient in decreasing the critical temperature arising from one-loop effective potential., Comment: V1: 39 pages, 2 figures, 2 tables, LaTeX format; V2: 53 pages, 3 figures, 1 table, Sect. IV revised, results are unchanged, 3 appendices and references added, version accepted for publication in Phys. Rev. D

The static Coulomb potential of Quantum Electrodynamics (QED) is calculated in the presence of a strong magnetic field in the lowest Landau level (LLL) approximation using two different methods. First, the vacuum expectation value of the corresponding Wilson loop is calculated perturbatively in two different regimes of dynamical mass $m_{dyn.}$, {\it i.e.}, $|{\mathbf{q}}_{\|}^{2}|\ll m_{dyn.}^{2}\ll |eB|$ and $m_{dyn.}^{2}\ll |\mathbf{q}_{\|}^{2}|\ll|eB|$, where $\mathbf{q}_{\|}$ is the longitudinal components of the momentum relative to the external magnetic field $B$. The result is then compared with the static potential arising from Born approximation. Both results coincide. Although the arising potentials show different behavior in the aforementioned regimes, a novel dependence on the angle $\theta$ between the particle-antiparticle's axis and the direction of the magnetic field is observed. In the regime $|{\mathbf{q}}_{\|}^{2}|\ll m_{dyn.}^{2}\ll |eB|$, for strong enough magnetic field and depending on the angle $\theta$, a qualitative change occurs in the Coulomb-like potential; Whereas for $\theta=0,\pi$ the potential is repulsive, it exhibits a minimum for angles $\theta\in]0,\pi[$., Comment: V1: 26 pages, 8 figures, latex format, V2: Accepted for publication in PRD (2007)

The Adler-Bell-Jackiw (ABJ) anomaly of a 3+1 dimensional QED is calculated in the presence of a strong magnetic field. It is shown that in the regime with the lowest Landau level (LLL) dominance a dimensional reduction from D=4 to D=2 dimensions occurs in the longitudinal sector of the low energy effective field theory. In the chiral limit, the resulting anomaly is therefore comparable with the axial anomaly of a two dimensional massless Schwinger model. It is further shown that the U(1) axial anomaly of QED in a strong magnetic field is closely related to the ``nonplanar'' axial anomaly of a conventional noncommutative QED., Comment: 18 pp, no figure. v2: The version accepted to be publidhed in PRD

In the presence of a strong magnetic field, the effective action of a composite scalar field in an scalar O(N) model is derived using two different methods. First, in the framework of worldline formalism, the 1PI n-point vertex function for the composites is determined in the limit of strong magnetic field. Then, the n-point effective action of the composites is calculated in the regime of lowest Landau level dominance. It is shown that in the limit of strong magnetic field, the results coincide and an effective field theory arises which is comparable with the conventional noncommutative field theory. In contrast to the ordinary case, however, the UV/IR mixing is absent in this modified noncommutative field theory., Comment: Latex file, 19 pp, no figure

Invariant (nonplanar) anomaly of noncommutative QED is reexamined. It is found that just as in ordinary gauge theory UV regularization is needed to discover anomalies, in noncommutative case, in addition, an IR regularization is also required to exhibit existence of invariant anomaly. Thus resolving the controversy in the value of invariant anomaly, an expression for the unintergrated anomaly is found. Schwinger terms of the current algebra of the theory are derived., Comment: LaTeX, axodraw.sty, 1 figure; v2: Typos corrected, References added, Version to appear in Int. J. Mod. Phys. A (2006)

Perturbative corrections to N=1/2 supersymmetric U(N) gauge theory at one-loop order are studied. It is shown that whereas the quantum corrections to N=1 sector of the theory are not affected by the C-deformation, the non(anti)commutativity parameter C receives one-loop perturbative corrections. These perturbative corrections are computed by performing an explicit one-loop calculation of the three and four-point functions of the theory. The running of the non(anti)commutativity parameter C is also studied using an appropriate Callan-Symanzik equation., Comment: 22 pages, latex file, V2: Typos corrected, Refs added

The Konishi anomalies for noncommutative N=1 supersymmetric U(1) gauge theory arising from planar and nonplanar diagrams are calculated. Whereas planar Konishi anomaly is the expected \star-deformation of the commutative anomaly, nonplanar anomaly reflects the important features of nonplanar diagrams of noncommutative gauge theories, such as UV/IR mixing and the appearance of nonlocal open Wilson lines. We use the planar and nonplanar Konishi anomalies to calculate the effective superpotential of the theory. In the limit of vanishing |\Theta p|, with \Theta the noncommutativity parameter, the noncommutative effective superpotential depends on a gauge invariant superfield, which includes supersymmetric Wilson lines, and has nontrivial dependence on the gauge field supermultiplet., Comment: LaTeX, 36 pages. Version 2: Typos Corrected. Version 3: Extensively revised version, 42 pages, to be published in Int. J. Mod. Phys. A. (2005)

In the first part of this work, a perturbative analysis up to one-loop order is carried out to determine the one-loop $\beta$-function of noncommutative U(1) gauge theory with matter fields in the adjoint representation. In the second part, the conformal anomaly of the same theory is calculated using the Fujikawa's path integral method. The value of the one-loop $\beta$-function calculated in both methods coincides. As it turns out, noncommutative QED with matter fields in the adjoint representation is asymptotically free for the number of flavor degrees of freedom $N_{f}<3$., Comment: 1+17 pages, LaTeX, axodraw.sty, 3 figures. Diploma thesis of M. Mohammadi. Email correspondence please to

The noncommutative dipole QED is studied in detail for the matter fields in the adjoint representation. The axial anomaly of this theory is calculated in two and four dimensions using various regularization methods. The Ward-Takahashi identity is proved by making use of a non-perturbative path integral method. The one-loop $\beta$-function of the theory is calculated explicitly. It turns out that the value of the $\beta$-function depends on the direction of the dipole length $\vec{L}$, which defines the noncommutativity. Finally using a semi-classical approximation a non-perturbative definition of the form factors is presented and the anomalous magnetic moment of this theory at one-loop order is computed., Comment: 1+30 pages, LaTeX, axodraw.sty, 7 figures

Anomalies arising from nonplanar triangle diagrams of noncommutative gauge theory are studied. Local chiral gauge anomalies for both noncommutative U(1) and U(N) gauge theories with adjoint matter fields are shown to vanish. For noncommutative QED with fundamental matters, due to UV/IR mixing a finite anomaly emerges from the nonplanar contributions. It involves a generalized $\star$-product of gauge fields., Comment: 28 pages, Latex, axodraw.sty; v2: version to appear in Int. J. Mod. Phys. A. (2001)

The axial anomaly of the noncommutative U(1) gauge theory is calculated by a number of methods and compared with the commutative one. It is found to be given by the corresponding Chern class., Comment: LaTeX, axodraw.sty; v2: typos are fixed; v3: version to appear in Int. J. Mod. Phys. A. (2001)

By carrying out a systematic expansion of Feynman integrals in the lattice spacing, we show that the axial anomaly in the U(1) lattice gauge theory with Wilson fermions, as determined in one-loop order from an irrelevant lattice operator in the Ward identity, must necessarily be identical to that computed from the dimensionally regulated continuum Feynman integrals for the triangle diagrams., Comment: 1 figure, LaTeX, 18 pages

A lattice action for QED is considered, where the derivatives in the Dirac operator are replaced by one-sided lattice differences. A systematic expansion in the lattice spacing of the one-loop contribution to the fermion self energy, vacuum polarization tensor and vertex function is carried out for an arbitrary choice of one-sided lattice differences. It is shown that only the vacuum polarization tensor possesses the correct continuum limit, while the fermion self energy and vertex function receive non-covariant contributions. A lattice action, discretized with a fixed choice of one-sided lattice differences therefore does not define a renormalizable field theory. The non-covariant contributions can however be eliminated by averaging the expressions over all possible choices of one-sided lattice differences., Comment: 3 figures, Latex, revised version: Addition of a reference, and of a sentence in the abstract and conclusion