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We give a pedagogical introduction to black holes (BHs) greybody factors (GFs) and quasinormal modes (QNMs) and share the recent developments on those subjects. To this end, we present some particular analytical and approximation techniques for the computations of the GFs and QNMs. We first review the gravitational GFs and show how they are analytically calculated for static and spherically symmetric higher dimensional BHs, consisting the charged BHs and existence of cosmological constant (i.e. de Sitter (dS)/anti-de Sitter (AdS)AdS BHs). The computations performed involve both the low-energy (having real and small frequencies) and the asymptotic (having extremely high frequency of the scattered wave throughout the imaginary axis) cases. A generic method is discussed at low frequencies. This method can be used for all three types of spacetime asymptotics and it is unaffected by the BH's features. For asymptotically dS BHs, GF varies depending on whether the spacetime dimension is even or odd, and is proportional to the ratio of the event and cosmic horizon areas. At asymptotic frequencies, the GFs can be computed by using a matching technique inspired by the monodromy method. In the meantime, we also make a general literature review on the matching technique in a separate section. While the GFs for charged or asymptotically dS BHs are generated by nontrivial functions, the GF for asymptotically AdS BHs is precisely one: pure black-body emission. QNMs, which are solutions to the relevant perturbation equations that satisfy the boundary conditions for purely outgoing (gravitational) waves at spatial infinity and purely ingoing (gravitational) waves at the event horizon, are considered using some particular analytical (like the matching technique) and approximation methods. In this study, our primary focus will be on the bosonic and fermionic GFs and QNMs of various BH and brane geometries and reveal the fingerprints of the invisibles with the radiation spectra to be obtained by the WKB approximation and bounding the Bogoliubov coefficients (together with the Miller-Good transformation) methods. [ABSTRACT FROM AUTHOR]

We consider a discrete-time non-Hamiltonian dynamics of a quantum system consisting of a finite sample locally coupled to several bi-infinite reservoirs of fermions with a translation symmetry. In this setup, we compute the asymptotic state, mean fluxes of fermions into the different reservoirs, as well as the mean entropy production rate of the dynamics. Formulas are explicitly expanded to leading order in the strength of the coupling to the reservoirs. [ABSTRACT FROM AUTHOR]

We derive the interaction of fermions with a dynamical space–time based on the postulate that the description of physics should be independent of the reference frame, which means to require the form‐invariance of the fermion action under diffeomorphisms. The derivation is worked out in the Hamiltonian formalism as a canonical transformation along the line of non‐Abelian gauge theories. This yields a closed set of field equations for fermions, unambiguously fixing their coupling to dynamical space–time. We encounter, in addition to the well‐known minimal coupling, anomalous couplings to curvature and torsion. In torsion‐free geometries that anomalous interaction reduces to a Pauli‐type coupling with the curvature scalar via a spontaneously emerged new coupling constant with the dimension of mass. A consistent model Hamiltonian for the free gravitational field and the impact of its functional form on the structure of the dynamical geometry space–time is discussed. [ABSTRACT FROM AUTHOR]

We consider interactions of scalar particles, photons, and fermions in Schwarzschild, Reissner–Nordström, Kerr, and Kerr–Newman gravitational and electromagnetic fields with a zero and nonzero cosmological constant. We also consider interactions of scalar particles, photons, and fermions with nonextremal rotating charged black holes in a minimal five-dimensional gauge supergravity. We analyze the behavior of effective potentials in second-order relativistic Schrödinger-type equations. In all cases, we establish the existence of the regime of particles "falling" on event horizons. An alternative can be collapsars with fermions in stationary bound states without a regime of particles "falling." [ABSTRACT FROM AUTHOR]

In this work, the Dirac equation is studied in the z = 0 Lifshitz black hole (Z 0 LBH) spacetime. The set of equations representing the Dirac equation in the Newman–Penrose (NP) formalism is decoupled into a radial set and an angular set. The separation constant is obtained with the aid of the spin weighted spheroidal harmonics. The radial set of equations, which are independent of mass, is reduced to Zerilli equations (ZEs) with their associated potentials. In the near horizon (NH) region, these equations are solved in terms of the Bessel functions of the first and second kinds arising from the fermionic perturbation on the background geometry. For computing the boxed quasinormal modes (BQNMs) instead of the ordinary quasinormal modes (QNMs), we first impose the purely ingoing wave condition at the event horizon. Then, Dirichlet boundary condition (DBC) and Newmann boundary condition (NBC) are applied in order to get the resonance conditions. For solving the resonance conditions, we follow the Hod's iteration method. Finally, Maggiore's method (MM) is employed to derive the entropy/area spectra of the Z 0 LBH which are shown to be equidistant. [ABSTRACT FROM AUTHOR]

For a model of decaying dark energy with a fermion (τ-lepton), additional corrections to the classical estimate of the time of falling of particles into a static uncharged black hole in Kramer's coordinates have been obtained, along with corrections to the Kruskal coordinates determined by a prescribed velocity functional of the fifth dimension. [ABSTRACT FROM AUTHOR]

Abstract The relativistic quantum mechanics of two interacting particles is considered. We first present a covariant formulation of kinematics and of reduced phase space, giving a short outline of the classical results. We then quantize the systems for the scalar–scalar, fermion–scalar and fermion–fermion cases. We study the spectrum and the spherical waves solutions of the free case. The interaction with central scalar and vector potentials is introduced and the explicit equations are deduced. The one particle and the non relativistic limits are recovered and the general lines for the solution of the boundary value problems are given. We make a numerical analysis of the first two cases with Coulomb interaction. For the two fermions we largely revisit the model we had previously derived in order to uniformize the description for all the three cases. In order to give a complete review we report in the Appendix some of the most interesting results obtained for atomic and mesonic systems with Coulomb and Cornell potential interactions respectively. [ABSTRACT FROM AUTHOR]

In this paper we study unitary braid group representations associated with Majorana Fermions. Majorana Fermions are represented by Majorana operators, elements of a Clifford algebra. The paper recalls and proves a general result about braid group representations associated with Clifford algebras, and compares this result with the Ivanov braiding associated with Majorana operators. The paper generalizes observations of Kauffman and Lomonaco and of Mo-Lin Ge to show that certain strings of Majorana operators give rise to extraspecial 2-groups and to braiding representations of the Ivanov type. [ABSTRACT FROM AUTHOR]

The paper studies the spinorial wave equations, namely the Dirac and the Klein–Gordon equations, as well as the greybody radiations and quasinormal modes (QNMs) of the charged Taub NUT black hole (CTNBH). To obtain fermionic greybody factors (GFs) and QNMs, we study the charged fermions by employing the Dirac equation. To this end, we use a null tetrad in the Newman–Penrose formalism. Then, we separate the Dirac equation into radial and angular sets. Using the obtained radial equations, we convert them into the typical one dimensional Schrödinger-like wave equations with the aid of tortoise coordinate and derive the effective potentials. For bosonic GFs and QNMs, we study the Klein–Gordon equation in the CTNBH geometry and obtain the radial equation. We then derive the effective potential and investigate the effect of NUT parameter on it. We show that while the fermionic QNMs and GFs individually increase with the increasing NUT parameter, the increase of bosonic GFs with increasing NUT parameter is overwhelmingly greater than that of the bosonic QNMs. [ABSTRACT FROM AUTHOR]

We investigate a model for the universe based on the self-interacting fermionic tachyon field. We have shown that by devising a self-interaction potential of a proper form, the fermionic tachyon field is capable of producing an accelerating expansion. At late times, this potential tends to a constant value; this behavior is consistent with the cosmological constant. In this way, the introduced fermionic tachyon field can be interpreted as the source of dark energy. • The fermionic tachyon field can account for the universe's accelerated expansion. • A self-interaction potential produced by four-fermion interactions is crucial in producing accelerated expansion. • At large times, its behavior is similar to the cosmological constant means the acceleration approaches a constant value. [ABSTRACT FROM AUTHOR]

The results of calculation of two-point correlation functions of fermionic currents in a constant uniform magnetic field are presented. The off-diagonal correlation functions including the tensor current (namely, the scalar-tensor and pseudoscalar-tensor) are calculated in addition to the correlators of scalar, pseudoscalar, vector, and axial-vector fermionic currents. The tensor fermionic current is a part of the Pauli term in the Lagrangian, which is responsible for the electromagnetic interaction of the fermion through an anomalous magnetic moment. In particular, if we take this interaction into account, we modify the frequency of axion-photon oscillations. In the future, it is planned to investigate this feature in details. [ABSTRACT FROM AUTHOR]

We examine a suggested relation between stochastic quantization and the holographic Wilsonian renormalization group in the massive fermion case on Euclidean AdS space. The original suggestion about the general relation between the two theories is posted in arXiv:1209.2242. In the previous researches, it is already verified that scalar fields, U(1) gauge fields, and massless fermions are consistent with the relation. In this paper, we examine the relation in the massive fermion case. Contrary to the other case, in the massive fermion case, the action needs particular boundary terms to satisfy boundary conditions. We finally confirm that the proposed suggestion is also valid in the massive fermion case. [ABSTRACT FROM AUTHOR]

We study the Dirac and the chargeless Klein–Gordon–Fock equations in the geometry of Grumiller’s spacetime that describes a model for gravity of a central object at large distances. The Dirac equation is separated into radial and angular equations by adopting the Newman–Penrose formalism. The angular part of the both wave equations are analytically solved. For the radial equations, we managed to reduce them to one dimensional Schrödinger-type wave equations with their corresponding effective potentials. Fermions’s potentials are numerically analyzed by serving their some characteristic plots. We also compute the quasinormal frequencies of the chargeless and massive scalar waves. With the aid of those quasinormal frequencies, Bekenstein’s area conjecture is tested for the Grumiller black hole. Thus, the effects of the Rindler acceleration on the waves of fermions and scalars are thoroughly analyzed. [ABSTRACT FROM AUTHOR]

A relation between the jump of spin and the corresponding jump of energy is derived. This relation is used to determine the binding energy of the nucleus and the “entanglement” energy between two bosons. The latter is shown to be inversely proportional to the area in the two-dimensional case. [ABSTRACT FROM AUTHOR]

In this paper, we study analytical solutions for fermion localization in Randall-Sundrum (RS) models. We show that there exist special couplings between scalar fields and fermions giving us discrete massive localizable modes. Besides this we obtain resonances in some models by analytical methods. [ABSTRACT FROM AUTHOR]

In this paper, we study unitary braid group representations associated with Majorana fermions. Majorana fermions are represented by Majorana operators, elements of a Clifford algebra. The paper proves a general result about braid group representations associated with Clifford algebras and compares this result with the Ivanov braiding associated with Majorana operators and with other braiding representations associated with Majorana fermions such as the Fibonacci model for universal topological quantum computing. [ABSTRACT FROM AUTHOR]

We give an exposition of iterant algebra, a generalization of matrix algebra that is motivated by the structure of measurement for discrete processes. We show how Clifford algebras and matrix algebras arise naturally from iterants, and we then use this point of view to discuss the Schrödinger and Dirac equations, Majorana Fermions, representations of the braid group and the framed braids in relation to the structure of the Standard Model for physics. [ABSTRACT FROM AUTHOR]

In this work we solve the sign problem of a frustrated quantum impurity model consisting of three quantum spin-half chains interacting through an anti-ferromagnetic Heisenberg interaction at one end. We first map the model into a repulsive Hubbard model of spin-half fermions hopping on three independent one dimensional chains that interact through a triangular hopping at one end. We then convert the fermion model into an inhomogeneous one dimensional model and express the partition function as a weighted sum over fermion worldline configurations. By imposing a pairing of fermion worldlines in half the space we show that all negative weight configurations can be eliminated. This pairing naturally leads to the original frustrated quantum spin model at half filling and thus solves its sign problem. [ABSTRACT FROM AUTHOR]

By introducing the commonly utilized Fe atoms into a two-dimensional (2D) honeycomb boron network, we theoretically designed a new Dirac material of FeB2 monolayer with a Fermi velocity in the same order of graphene. The electron transfer from Fe atoms to B networks not only effectively stabilizes the FeB2 networks but also leads to the strong interaction between the Fe and B atoms. The Dirac state in FeB2 system primarily arises from the Fe d orbitals and hybridized orbital from Fe-d and B-p states. The newly predicted FeB2 monolayer has excellent dynamic and thermal stabilities and is also the global minimum of 2D FeB2 system, implying its experimental feasibility. Our results are beneficial to further uncovering the mechanism of the Dirac cones and providing a feasible strategy for Dirac materials design. [ABSTRACT FROM AUTHOR]

We study the vacuum polarization of zero-mass charged fermions in Coulomb and Aharonov-Bohm potentials in 2+1 dimensions. For this, we construct the Green's function of the two-dimensional Dirac equation in the considered field configuration and use it to find the density of the induced vacuum charge in so-called subcritical and supercritical regions. The Green's function is represented in regular and singular (in the source) solutions of the Dirac radial equation for a charged fermion in Coulomb and Aharonov-Bohm potentials in 2+1 dimensions and satisfies self-adjoint boundary conditions at the source. In the supercritical region, the Green's function has a discontinuity related to the presence of singularities on the nonphysical sheet of the complex plane of 'energy,' which are caused by the appearance of an infinite number of quasistationary states with negative energies. Ultimately, this situation represents the neutral vacuum instability. On the boundary of the supercritical region, the induced vacuum charge is independent of the self-adjoint extension. We hope that the obtained results will contribute to a better understanding of important problems in quantum electrodynamics and will also be applicable to the problem of screening the Coulomb impurity due to vacuum polarization in graphene with the effects associated with taking the electron spin into account. [ABSTRACT FROM AUTHOR]

In this paper, we realize the Lie algebra in one homotopy category, and we find that tau functions can be obtained from complexes in this homotopy category by taking Grothendieck group. We start with the realization of Fermions in a homotopy category over a Heisenberg category which is constructed by Khovanov. [ABSTRACT FROM AUTHOR]

Pair particle creation is a well-known effect in the domain of field theory in curved space-time. The behavior of the generated entanglement due to expanding universe is very different for spin-0 and spin-1/2 particles. We study spin-1 particles in Friedmann-Robertson-Walker (FRW) space-time using Duffin-Kemmer-Petiau equation and spin-3/2 particles in FRW space-time using Rarita-Schwinger equation. We find that in expanding universe, the behavior of the generated entanglement for spin-1 particles is the same as the behavior of the generated entanglement for spin-0 particles. Also, we find that spin-3/2 and spin-1/2 particles have the same behavior for the generated entanglement in expanding universe. We conclude that the absolute values of spins do not play any role and the differences in the behavior of the generated entanglement in expanding universe are due to bosonic or fermionic properties. [ABSTRACT FROM AUTHOR]

On the basis of a microscopic model of self-consistent field, the thermodynamics of the many-particle Fermi system at finite temperatures with account of three-body interactions is built and the quasiparticle equations of motion are obtained. It is shown that the delta-like three-body interaction gives no contribution into the self-consistent field, and the description of three-body forces requires their nonlocality to be taken into account. The spatially uniform system is considered in detail, and on the basis of the developed microscopic approach general formulas are derived for the fermion's effective mass and the system's equation of state with account of contribution from three-body forces. The effective mass and pressure are numerically calculated for the potential of "semi-transparent sphere" type at zero temperature. Expansions of the effective mass and pressure in powers of density are obtained. It is shown that, with account of only pair forces, the interaction of repulsive character reduces the quasiparticle effective mass relative to the mass of a free particle, and the attractive interaction raises the effective mass. The question of thermodynamic stability of the Fermi system is considered and the three-body repulsive interaction is shown to extend the region of stability of the system with the interparticle pair attraction. The quasiparticle energy spectrum is calculated with account of three-body forces. [ABSTRACT FROM AUTHOR]

A quantum game is described making use of coins embodied as entangled Fermions in a potential energy well. It is shown that the odds are affected by the Pauli Exclusion Principle. They depend on the elevation in the energy well where the coins are selected, ranging from being a certainty of winning at the bottom of the well to being near classical at the top. These odds differ markedly from those in a classical game in which they are independent of elevation. The thermodynamics counterpart of the quantum game is discussed. It is shown that the temperature of a Maxwellian gas column in a potential energy gradient is independent of elevation. However, the temperature of a Fermion gas is shown to drop with elevation. The game and the gas column utilize the same components. When Fermions are used, a shifting of odds is produced in the game and a shifting of kinetic energy is produced in the thermodynamic experiment, leading to a spontaneous temperature gradient. [ABSTRACT FROM AUTHOR]

We discuss the coherent state of an attractive superfluid Fermi gas. In order to explain the time evolution of the Fermi atomic gas in the optical lattice, we present mathematical relations for the autocorrelation function and first-order correlation function. The analytical results show a dependence of the oscillation time on the controlling parameters, which may be achieved experimentally. [ABSTRACT FROM AUTHOR]

We aim in this paper to study Brans-Dicke cosmology in the presence of varying mass fermions and a self-interaction potential. Furthermore, we also probe the entropy corrected holographic dark energy (ECHDE) in the model in two non-interacting and interacting scenarios. The model parameters are constrained by using the recent SNe Ia observational data and tested against observational data of Hubble parameter. For a comparison, we also constrained and tested the cosmological parameters in ΛCDM model with the same observational data. We show that in non of the scenarios the model prediction is better than ΛCDM model. [ABSTRACT FROM AUTHOR]

Interaction between particles in condensate state is nontrivial in understanding charge pairing that defines high-temperature superconductivity. A Bose-Einstein Condensate (BEC) of a non-zero-momentum Cooper pair constitutes a composite boson. A two-component electronic BEC - bosons and fermions - harbours some properties that are closely related to those of high temperature superconductors. We demonstrated that quantum coherence of a boson-fermion condensate is controlled by plasmons. A binary electronic system has an associated response function, given by the zero of longitudinal dielectric function. The response function has both long and short-wavelength branches, at least in layered superconductors. Coulomb screening of bosons by the electron cloud, in the long-wavelength branch, drives plasmon mediation in boson-fermion (BF) pairing. This study reveals that: the attractive potential in boson-fermion pair condensate (BFPC) is anisotropic, the magnitude of collective BEC excitations is in the order of an energy gap and that boson-fermion coherence under plasmon-mediation occurs at 10 − 9 m. • We study the electronic boson-fermion interactions in the Bose-Einstein Condensate (BEC) state under plasmon mediation. • The collective excitation of electronic BFP condensates is anisotropic. • The magnitude of collective excitation of electronic BFP condensates is in the order of energy gaps of high temperature superconductors. • Plasmons can sufficiently mediate boson-fermion coherence over 10−9 m. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of fermion creation inside a three-dimensional cubic box. We present an appropriate wave function which satisfies the Dirac equation in this geometry with MIT bag model boundary condition. We consider the box with oscillating walls and introduce the time evolution of the quantized field by expanding it over the instantaneous basis. We explain how we can obtain the average number of particles created. In this regard, we find the Bogoliubov coefficients. We consider an oscillation and determine the coupling conditions between different modes that can be satisfied depending on the cavity's spectrum. Assuming the parametric resonance case we obtain an expression for the mean number of created fermions in each mode of an oscillation and their dynamical Casimir energy. [ABSTRACT FROM AUTHOR]

-1 The boson images of fermion SO(2N+1) Lie operators have been given together with those of SO(2N+2) ones. The SO(2N+1) Lie operators are generators of rotation in the (2N+1)-dimensional Euclidean space (N: number of single-particle states of the fermions). The images of fermion annihilation-creation operators must satisfy the canonical anticommutation relations, when they operate on a spinor subspace. In the regular representation space we use a boson Hamiltonian with Lagrange multipliers to select out the spinor subspace. Based on these facts, a new description of a fermionic SO(2N+2) top is proposed. From the Heisenberg equations of motions for the boson operators, we get the SO(2N+1) self-consistent field (SCF) Hartree-Bogoliubov (HB) equation for the classical stationary motion of the fermion top. Decomposing an SO(2N+1) matrix into matrices describing paired and unpaired modes of fermions, we obtain a new form of the SO(2N+1) SCF equation with respect to the paired-mode amplitudes. To demonstrate the effectiveness of the new description based on the bosonization theory, the extended HB eigenvalue equation is applied to a superconducting toy-model which consists of a particle-hole plus BCS-type interaction. It is solved to reach an interesting and exciting solution which is not found in the traditional HB eigenvalue equation due to the unpaired-made effects. To complete the new description, the Lagrange multipliers must be determined in the classical limit. For this aim a quasi-anticommutation relation approximation is proposed. Only if a certain relation between an SO(2N+1) parameter z and the N is satisfied, unknown parameters K and l in the Lagrange multipliers can be determined without any inconsistency. [ABSTRACT FROM AUTHOR]

In this paper, we calculate the Casimir energy for a massive fermionic field confined between two points in one spatial dimension, with the MIT bag model boundary condition. We compute the Casimir energy directly by summing over the allowed modes. The method that we use is based on the Boyer's method, and there will be no need to resort to any analytic continuation techniques. We explicitly show the graph of the Casimir energy as a function of the distance between the points and the mass of the fermionic field. We also present a rigorous derivation of the MIT bag model boundary condition. [ABSTRACT FROM AUTHOR]

The extension of study done in a previous work about the dilaton mean field stabilization thanks to the potential generated by massive fermions, is reviewed. Three loop corrections were evaluated in addition to the previously calculated two loop terms. The results indicate that the dilaton vacuum field tend to be fixed at a high value close to the Planck scale, in accordance with the need for predicting Einstein gravity from string theory. Moreover, the mass of the dilaton is evaluated to be also a high value close to the Planck mass, which implies the absence of dilaton scalar signals in modern cosmological observations. These properties arise when the fermion mass is chosen to be either at a lower bound corresponding to the top quark mass, or alternatively, at a very much higher value assumed to be in the grand unification energy range. [ABSTRACT FROM AUTHOR]

Abstract: Extending our earlier study of nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for one fermionic mode, in the present paper, we perform a thorough study of general (nonlinear) canonical transformations for two fermionic modes. We find that the Bogolyubov-Valatin group for fermionic modes, which can be implemented by means of unitary transformations, is isomorphic to . The investigation touches on a number of subjects. As a novelty from a mathematical point of view, we study the structure of nonlinear basis transformations in a Clifford algebra [specifically, in the Clifford algebra ] entailing (supersymmetric) transformations among multivectors of different grades. A prominent algebraic role in this context is being played by biparavectors (linear combinations of products of Dirac matrices, quadriquaternions, sedenions) and spin bivectors (antisymmetric complex matrices). The studied biparavectors are equivalent to Eddington’s -numbers and can be understood in terms of the tensor product of two commuting copies of the division algebra of quaternions . From a physical point of view, we present a method to diagonalize any arbitrary two-fermion Hamiltonians. Relying on Jordan-Wigner transformations for two-spin- and single-spin- systems, we also study nonlinear spin transformations and the related problem of diagonalizing arbitrary two-spin- and single-spin- Hamiltonians. Finally, from a calculational point of view, we pay due attention to explicit parametrizations of and matrices (of respective sizes 4×4 and 6×6) and their mutual relation. [Copyright &y& Elsevier]

Abstract: A proof of the quantum H-theorem in the context of Kaniadakis'' entropy concept and a generalization of stosszahlansatz are presented, showing that there exists a quantum version of the second law of thermodynamics consistent with the Kaniadakis statistics. It is also shown that the marginal equilibrium states are described by quantum κ-power law extensions of the Fermi–Dirac and Bose–Einstein distributions. [Copyright &y& Elsevier]

The classical matter fields are sections of a vector bundle E with base manifold M, and the space L2( E) of square integrable matter fields w.r.t. a locally Lebesgue measure on M, has an important module action of $${C_b^\infty(M)}$$ on it. This module action defines restriction maps and encodes the local structure of the classical fields. For the quantum context, we show that this module action defines an automorphism group on the algebra of the canonical anticommutation relations, CAR( L2( E)), with which we can perform the analogous localization. That is, the net structure of the CAR( L2( E)) w.r.t. appropriate subsets of M can be obtained simply from the invariance algebras of appropriate subgroups. We also identify the quantum analogues of restriction maps, and as a corollary, we prove a well–known “folk theorem,” that the CAR( L2( E)) contains only trivial gauge invariant observables w.r.t. a local gauge group acting on E. [ABSTRACT FROM AUTHOR]

A new formulation of perturbation theory for a description of the Dirac and scalar fields (the Yukawa model) is suggested. For a main approximation, the self-consistent field model that considers to a certain degree forces caused by interaction of fields is chosen. This approximation leads to a normally ordered form of the interaction Hamiltonian. Generation of fermion mass in the process of interaction with exchange by a scalar boson is investigated. It is demonstrated that for zero bare mass, the fermion can acquire mass only if its coupling constant exceeds the critical value determined by the boson mass. In this regard, the problem of the neutrino mass is discussed. [ABSTRACT FROM AUTHOR]

In its bare and natural form, the Dirac Equation describes only spin-1/2 particles. The main purpose of this reading is to make a valid and justified mathematical modification to the Dirac Equation so that it describes any spin particle. We show that this mathematical modification is consistent with the Special Theory of Relativity (STR). From the vantage point of unity, simplicity and beauty, it is natural to wonder why should there exist different equations to describe particles of different spins? For example, the Klein-Gordon equation describes spin-0 particles, while the Dirac Equation describes spin-1/2, and the Rarita-Schwinger Equation describes spin-3/2. Does it mean we have to look for another equation to describe spin-2 particles, and then spin-5/2 particles etc? This does not look beautiful, simple, or at the very least suggest a Unification of the Natural Laws. [ABSTRACT FROM AUTHOR]

Bosonic and fermionic particle currents can be introduced in a more unified way, with the cost of introducing a preferred spacetime foliation. Such a unified treatment of bosons and fermions naturally emerges from an analogous superstring current, showing that the preferred spacetime foliation appears only at the level of effective field theory, not at the fundamental superstring level. The existence of the preferred spacetime foliation allows an objective definition of particles associated with quantum field theory in curved spacetime. Such an objective definition of particles makes the Bohmian interpretation of particle quantum mechanics more appealing. The superstring current allows a consistent Bohmian interpretation of superstrings themselves, including a Bohmian description of string creation and destruction in terms of string splitting. The Bohmian equations of motion and the corresponding probabilistic predictions are fully relativistic covariant and do not depend on the preferred foliation. [ABSTRACT FROM AUTHOR]

The interaction of a fermion with the dense axion medium is investigated for the purpose of finding an axion medium effect on the fermion dispersion. It is shown that axion medium influence on the fermion dispersion under astrophysical conditions is negligible small if the correct Lagrangian of the axion–fermion interaction is used. [ABSTRACT FROM AUTHOR]

Abstract: For a system of charged Fermions interacting with an electromagnetic field, we derive a non-Markovian master equation in the second-order approximation of the weak dissipative coupling. A complex dissipative environment including Fermions, Bosons and the free electromagnetic field is taken into account. Besides the well-known Markovian term of Lindblad’s form, that describes the decay of the system by correlated transitions of the system and environment particles, this equation includes new Markovian and non-Markovian terms proceeding from the fluctuations of the self-consistent field of the environment. These terms describe fluctuations of the energy levels, transitions among these levels stimulated by the fluctuations of the self-consistent field of the environment, and the influence of the time-evolution of the environment on the system dynamics. We derive a complementary master equation describing the environment dynamics correlated with the dynamics of the system. As an application, we obtain non-Markovian Maxwell–Bloch equations and calculate the absorption spectrum of a field propagation mode transversing an array of two-level quantum dots. [Copyright &y& Elsevier]

We consider the transition to temperature-dependent equations for ultrasecond-quantized problems. [ABSTRACT FROM AUTHOR]

We show that the superfluidity phenomenon occurs for classical liquids in nanotubes. [ABSTRACT FROM AUTHOR]

The retarded interaction between an electron and a spin-0 nucleus, that has been derived from electro--dynamical perturbation theory is discussed here. A brief account of the derivation is given. The retarded form is correct through order v²/c². Use of the relative coordinates leads to an effective oneelectron operator that can be used through all orders of perturbation theory. A few unitary transformations give rise to the interaction that is valid in the non-relativistic limit. [ABSTRACT FROM AUTHOR]

We report the electronic structure of the crystalline solid CeCoGe2 through the approximation TB-LMTO-ASA at level LSDA (In the parametrization of von Barth-Hedin) and LSDA (vBH)+U (Local Spin Density Approximation-von Barth-Hedin + Hubbard correction term) within the fra-mework of the DFT theory. The optimized cell parameter using the theory of the pseudopotentials, calculating its density of states, and band structures. The material presents theoretical a metallic and no-magnetic behavior at LSDA level, but changing to magnetic state at LSDA+U approximation having then heavy fer-mion characteristics. [ABSTRACT FROM AUTHOR]

We begin by considering a system which gives the usual fermion algebra when the appropriate limiting case is considered. We study its Hopf algebra structure. Investigation of its representation forces us to impose additional constraints on the system such that by defining a central hermitian operator s in terms of the operators defining the system, we obtain s-deformed particle algebra. Finally, we find a formula for the addition of s values for the d = 2 case. [ABSTRACT FROM AUTHOR]

Abstract: The interest in trapping of cold particles and other low-energy phenomena has stimulated research on threshold processes for three body systems. Such processes are efficiently modeled using the adiabatic hyperspherical representation. For threshold processes the behavior of the adiabatic curves at large hyperradius play a crucial role. These curves may be modeled using energy dependent zero range potentials. We employ such potentials for the case of three fermions where the two-body systems can be bound in p-wave bound states. Calculated adiabatic potential curves are presented. [Copyright &y& Elsevier]

The de Broglie-Bohm interpretation of quantum mechanics and quantum field theory is generalized in such a way that it describes trajectories of relativistic fermionic particles and antiparticles and provides a causal description of the processes of their creation and destruction. A general method of causal interpretation of quantum systems is developed and applied to a causal interpretation of fermionic quantum field theory represented by e-number valued wave functionals. [ABSTRACT FROM AUTHOR]

The scattering theory for a class of fermionic Pauli–Fierz models is considered. We give a proof of the asymptotic completeness of the dynamics in the case of massive fermions. The result applied to the Hamiltonian of a quantized spin-1/2 Dirac particle interacting with an external field through a cutoff Yukawa interaction and to the Hamiltonian of a system of finitely many confined particles coupled to a fermionic field with a quadratic interaction. [Copyright &y& Elsevier]

We study the Casimir problem for a fermion coupled to a static background field in one space dimension. We examine the relationship between interactions and boundary conditions for the Dirac field. In the limit that the background becomes concentrated at a point (a “Dirac spike”) and couples strongly, it implements a confining boundary condition. We compute the Casimir energy for a masslike background and show that it is finite for a stepwise continuous background field. However the total Casimir energy diverges for the Dirac spike. The divergence cannot be removed by standard renormalization methods. We compute the Casimir energy density of configurations where the background field consists of one or two sharp spikes and show that the energy density is finite except at the spikes. Finally we define and compute an interaction energy density and the force between two Dirac spikes as a function of the strength and separation of the spikes. [Copyright &y& Elsevier]