Search

Institute of Theoretical Physics, University of Wroclaw,pl. M. Borna 9, 50–204 Wroclaw, Poland(Received January 4, 2007)We briefly review some issues of the nilpotent objects in theoretical physics using simple modelsas an illustration. Nilpotent elements appear at quantum and classical level in several ways. On theone hand there are celebrated BRST operators, external derivative and related with them cohomolo-gy theory, on the other hand there are dual numbers which are a less known structure than complexnumbers but important in many approaches, then there are commuting nilpotent variables, some-how generalizing the nilpotent but anticommuting Grassmann variables used in super-mathematicsand SUSY models. As an interesting fact we note that nilpotent variables demand the use of thegeneralized light-cone geometry with the metric of the null signature.Key words: infrared divergence, hydrodynamical approach, renormalization.PACS number(s): 11.30.Pb, 45.20.JjI. INTRODUCTION

The $H\to gg$ amplitude relevant for Higgs production via gluon fusion is computed in the four-dimensional helicity scheme (FDH) and in dimensional reduction (DRED) at the two-loop level. The required renormalization is developed and described in detail, including the treatment of evanescent $\epsilon$-scalar contributions. In FDH and DRED there are additional dimension-5 operators generating the $H g g$ vertices, where $g$ can either be a gluon or an $\epsilon$-scalar. An appropriate operator basis is given and the operator mixing through renormalization is described. The results of the present paper provide building blocks for further computations, and they allow to complete the study of the infrared divergence structure of two-loop amplitudes in FDH and DRED.

We study the ``Higgs'' amplitude mode in the relativistic quantum $\mathrm{O}(N)$ model in two space dimensions. Using the nonperturbative renormalization group and the Blaizot--M\'endez-Galain--Wschebor approximation (which we generalize to compute four-point correlation functions), we compute the $\mathrm{O}(N)$-invariant scalar susceptibility at zero temperature in the vicinity of the quantum critical point. In the ordered phase, we find a well-defined Higgs resonance for $N=2$ and 3 and determine its universal properties. No resonance is found for $N\ensuremath{\ge}4$. In the disordered phase, the spectral function exhibits a threshold behavior with no Higgs-like peak. We also show that for $N=2$, the Higgs mode manifests itself as a very broad peak in the longitudinal susceptibility in spite of the infrared divergence of the latter. We compare our findings with results from quantum Monte Carlo simulations and $\ensuremath{\epsilon}=4\ensuremath{-}(d+1)$ expansion near $d=3$.

Respecting the group theoretical approach, it is debated that the theory of linear conformal gravity should be formulated through a tensor field of rank-3 and mixed symmetry \cite{binegar}. Pursuing this path, such a field equation was obtained in de Sitter space \cite{takook}. In present work, considering the de Sitter ambient space notation, a proper solution to the physical part of this field equation is obtained. We have also calculated the related two-point function, which is interestingly de Sitter invariant and free of infrared divergence., 10 pages

Extensive investigations show that ${\mathrm{QED}}_{3}$ exhibits dynamical fermion mass generation at zero temperature when the fermion flavor $N$ is sufficiently small. However, it seems difficult to extend the theoretical analysis to finite temperature. We study this problem by means of the Dyson-Schwinger equation approach after considering the effect of finite temperature or disorder-induced fermion damping. Under the widely used instantaneous approximation, the dynamical mass displays an infrared divergence in both cases. We then adopt a new approximation that includes an energy-dependent gauge boson propagator and obtain results for dynamical fermion mass that do not contain infrared divergence. The validity of the new approximation is examined by comparing it to the well-established results obtained at zero temperature.

The quantization scheme based on reduction of the physical states \cite{Park:2014tia} is extended to two gravity-matter systems and pure dS gravity. For the gravity-matter systems we focus on quantization in a flat background for simplicity, and renormalizability is established through gauge-fixing of matter degrees of freedom. Quantization of pure dS gravity has several new novel features. It is noted that the infrared divergence does not arise in the present scheme of quantization. The lapse function constraint plays a crucial role., Comment: 39 pages, 1 figure, refs and clarifications added, version to appear in IJGMMP

The strong phases and CP violation in the rare $\bar{B}^0\to K^+K^-$, $K^{*\pm}K^\mp$, $K^{*+}K^{*-}$ decays are investigated. As these decays proceed only via annihilation type diagrams in the standard model (SM), a dynamical gluon mass is introduced to avoid the infrared divergence in the soft endpoint regions. The Cutkosky rule is adopted to deal with a physical-region singularity of the on mass-shell quark propagators, which leads to a big imaginary part and hence a large strong phase. As a consequence, large CP asymmetries are predicted in those decay modes due to a big interference between the annihilation amplitudes from penguin and tree operators, which may be tested in future more precise experiments.

Resume Nous proposons des bases bi-orthogonales d'ondelettes qui resolvent le probleme de la divergence infra-rouge des series en ondelettes usuelles dans les espaces de Sobolev homogenes H ˙ s ( R n ) . Ces bases permettent de supprimer la divergence dans le cas s − n 2 ∉ N car elles sont aussi des bases de la realisation de H ˙ s ( R n ) . Dans le cas critique s − n 2 ∈ N , elles fournissent un confinement de la divergence infra-rouge sur un « petit » espace. Cette methode de confinement s'applique aussi au processus de Mumford. Pour citer cet article : B. Vedel, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

In this Letter, we investigate the vertex corrections and spectator hard scattering contributions to B → χ c 0 , 2 K decays, which has no leading contribution from naive factorization scheme. A non-zero binding energy b = 2 m c − M is introduced to regularize the infrared divergence of the vertex part. The spectator diagrams also contain logarithmic and linear infrared divergences, for which we adopt a model dependent parametrization. If we neglect possible strong phases in the hard spectator contributions, we obtain a too small branching ratio for χ c 0 K while too large one for χ c 2 K , as can be seen from the ratio of the branching ratio of B + → χ c 2 K + to that of B + → χ c 0 K + , which is predicted to be 2.15 −0.76 +0.63 in our model, while experimentally it should be about 0.1 or even smaller. But a closer examination shows that, assuming large strong phases difference between the twist-2 and twist-3 spectator terms, together with a slightly larger spectator infrared cutoff parameter Λ h , it is possible to accommodate the experimental data. This shows that, for B → χ c 0 , 2 K decays with no factorizable contributions, QCDF seems capable of producing decay rates close to experiments, in contrast to the B → J / ψ K decay which is dominated by the factorizable contributions.

We present a factorization formula for valence quark distributions in a hadron in x-->1 limit. For the example of pion, we arrive at the form of factorization by analyzing momentum flow in the leading and high-order Feynman diagrams. The result confirms the well-known 1-x scaling rule to all orders in perturbation theory, providing the non-perturbative matrix elements for the infrared-divergence factors. We comment on re-summation of perturbative single and double logarithms in 1-x., 7 pages, 2 figures included

We calculate the anomalous magnetic moment of the electron in the Chern-Simons theory in 2+1 dimensions with and without a Maxwell term, both at zero temperature as well as at finite temperature. In the case of the Maxwell-Chern-Simons (MCS) theory, we find that there is an infrared divergence, both at zero as well as at finite temperature, when the tree level Chern-Simons term vanishes, which suggests that a Chern-Simons term is essential in such theories. At high temperature, the thermal correction in the MCS theory behaves as $\frac{1}{\beta} \ln \beta M$, where $\beta$ denotes the inverse temperature and $M$, the Chern-Simons coefficient. On the other hand, we find no thermal correction to the anomalous magnetic moment in the pure Chern-Simons (CS) theory., Comment: 13 pages, 2 figures

We study the exclusive decays of $B$ meson into P-wave charmonium states $\chi_{cJ}(J=0,1)$ in the QCD factorization approach with light-cone distribution functions describing the mesons in the processes. For $B \to \chi_{c1} K$ decay, we find that there are logarithmic divergences arising from nonfactorizable spectator interactions even at twist-2 order and the decay rate is too small to accommodate the experimental data. For $B\to \chi_{c0} K$ decay, we find that aside from the logarithmic divergences arising from spectator interactions at leading-twist order, more importantly, the factorization will break down due to the infrared divergence arising from nonfactorizable vertex corrections, which is independent of the specific form of the light-cone distribution functions. Our results may indicate that QCD factorization in the present form may not be safely applied to $B$-meson exclusive decays to charmonium states., Comment: Latex, 7 pages, 1 eps figure, final version to appear in Phys.Lett.B; a few references are added, the expression of chi_c1 decay constant is given

Multi-photon and coherent states of light are formulated in terms of a reducible representation of canonical commutation relations. Standard properties of such states are recovered as certain limiting cases. The new formalism leads to field operators and not operator-valued distributions. The example of radiation fields produced by a classical current shows an automatic regularization of the infrared divergence., version accepted in Phys. Lett. A

The dynamics of a particle which is linearly coupled to a boson field is investigated. The boson field induces superselection rules for the momentum of the particle, if the field is infrared divergent. Thereby the Hamiltonian of the total system remains bounded from below., 8 pages

14 págs,; 4 figs., © 2015, EDP Sciences and Springer. We describe a family of lattice models that support a new class of quantum magnetism characterized by correlated spin and bosonic ordering [Phys. Rev. Lett. 112, 180405 (2014)]. We explore the full phase diagram of the model using Matrix-Product-State methods. Guided by these numerical results, we describe a modified variational ansatz to improve our analytic description of the groundstate at low boson frequencies. Additionally, we introduce an experimental protocol capable of inferring the low-energy excitations of the system by means of Fano scattering spectroscopy. Finally, we discuss the implementation and characterization of this model with current circuit-QED technology., We acknowledge support from Spanish MINECO Project FIS2012- 33022, and CAM regional research consortium QUITEMAD S2009-ESP-1594.

Investigating the Bogoliubov-de Gennes equation, widely used in the analysis of Bose-Einstein condensate in neutral atomic gases, we reveal some aspect of the interplay between the zero and complex modes. The complex mode implies that the system is dynamically unstable. The zero modes originate from the spontaneous symmetry breakdown, but their roles are not clear because they cause the infrared divergence. In this paper, we deal with the system of a dark soliton in Bose-Einstein condensate which has two zero modes corresponding to the spontaneously broken U(1) gauge and translational symmetries, and show that the zero and its adjoint modes, associated with the spontaneous breakdown of translational symmetry, turn into pure imaginary modes under the perturbation which explicitly breaks translational symmetry.

Radiative effects in the electroproduction of photons in polarized $ep$-scattering are calculated with the next-to-leading (NLO) accuracy. The contributions of loops and two photon emission were presented in analytical form. The covariant approach of Bardin and Shumeiko was used to extract the infrared divergence. All contributions to the radiative correction were presented in the form of the correction to the leptonic tensor thus allowing for further applications in other experiments, e.g., deep inelastic scattering. The radiative corrections (RC) to the cross sections and polarization asymmetries were analyzed numerically for kinematical conditions of the current measurement at Jefferson Lab. Specific attention was paid on analyzing kinematical conditions for the process with large radiative effect when momenta of two photons in the final state are collinear to momenta of initial and final electrons, respectively., Comment: 22 pages, 7 figures, 4 appendices

We consider a model of quantum particles coupled to a massless quantum scalar field, called the massless Nelson model, in a non-Fock representation of the time-zero fields which satisfy the canonical commutation relations. We show that the model has a ground state for all values of the coupling constant even in the case where no infrared cutoff is made. The non-Fock representation used is inequivalent to the Fock one if no infrared cutoff is made.

Since b quark mass is not asymptotically large, chirally enhanced corrections which arise from twist-3 wave functions may be important in B decays. We thus evaluate the hadronic matrix elements with the final light pseudoscalar mesons described by leading twist and twist-3 distribution amplitudes. We find that chirally enhanced corrections can be included consistently in the framework of QCD factorization only if the twist-3 distribution amplitudes are symmetric. We then give explicit expressions of $a_i^p$ for $B \to \pi\pi$ at the next-to-leading order of $\alpha_s$ including chirally enhanced corrections. We also briefly discuss the divergence appeared in the hard spectator contributions., Comment: 12 pages, 3 figures, A revised version to appear in Phys. Lett. B

We calculate the d.c. Josephson current through charge density wave (CDW) region connected to two superconductors (S 1 , S 2 ) by tunnel junctions. At T =0 and without impurities, we discover infrared divergence in the d.c. Josephson current caused by the phase mode in the long-junction limit: d / v F ≫ℏ/ Δ S , ℏ/ Δ CDW where T is temperature. These limits are expressed by using the energy gap in S region Δ S , the length d , the Fermi velocity v F , and the energy gap Δ CDW in CDW region. The critical current is proportional to ( Δ CDW ℏ v F / d ) 1/2 ∝ Δ CDW ( ξ CDW / d ) 1/2 . At βΔ S ( T ), βΔ CDW ( T )≫1 and β ℏ v F / d ≪1, the T -dependence of the correction caused by the phase mode is T -linear where β =1/ k B T and k B is Boltzmann constant. At finite temperatures and with impurities, the correction caused by the phase mode becomes proportional to ln T . At finite temperatures and without impurities, the critical current is similar to the Ambegaokar–Baratoff formula which is proportional to Δ S ( T ) in the short-junction limit: d / v F ≪ℏ/ Δ S , ℏ/ Δ CDW .

We consider a model of quantum particles coupled to a massless quantum scalar field, called the massless Nelson model, in a non-Fock representation of the time­zero fields which satisfy the canonical commutation relations. We show that the model has a ground state for all values of the coupling constant even in the case where no infrared cutoff is made. The non-Fock representation used is inequivalent to the Fock one if no infrared cutoff is made.

The correct formulation of the two-time self-consistent Coulomb quantum kinetics with screening requires a polarization loop obeying the Ward identity stemming from the charge conservation. Otherwise an infrared divergence occurs. For a self-consistent self-energy without vertex part, a polarization loop which includes a vertex part calculated in the ladder approximation, is shown to satisfy the required Ward identity.

We have recently obtained cross-sections for Compton scattering by K-shell electrons at extreme-relativistic (ER) energies of the incoming photon. Our method is essentially analytical, and only at the end did it require a modest numerical computation. The results are valid for the Compton line of the scattered photon spectrum, but do not cover the infrared divergence at the soft-photon end of the spectrum. This case is treated in the present paper. The method we apply here is an adaptation of the one used for the Compton line. This allows us to make use of many previous results. The quadruply and doubly differential Compton cross-sections can be expressed in analytical forms which allow factorization of the ER photoeffect cross-sections (differential or total, respectively). This result is shown to be a manifestation of the soft-photon theorem connecting the Compton matrix element at low emitted photon frequencies to that of the photoeffect. The computation of ER Compton cross-sections with soft-photon emission is thereby reduced to that of the cross-sections for the ER photoeffect. We carry out a computation for the latter case and extend previously existing results.

This paper studies the model of the quantum electrodynamics (QED) of a single nonrelativistic electron due to W. Pauli and M. Fierz and studied further by P. Blanchard. This model exhibits infrared divergence in a very simple context. The infrared divergence is associated with the inequivalence of the Hilbert spaces associated with the free Hamiltonian and with the complete Hamiltonian. Infrared divergences that are visible in the perturbative description disappear in the space of the clothed electrons. In this model when the Hamiltonian is expressed in terms of the “physical” fields that create the electron together with its cloud of soft photons, the variational principle suggested earlier can be applied. At finite time the Heisenberg field of the model acts in the space of the perturbative electron together with a finite number of perturbative photons, while the “physical” field can be chosen to act in the space of the exact (“physical”) electron eigenstates together with a finite number of physical photons. The space of the physical (or clothed) electron states can be chosen to be a Fock space.

As a straightforward extention of the study on infrared divergences in pseudo-particle spectra in the single-channel degenerate impurity Anderson model, those of the multichannel model are examined with use of the expansion from the large limit of the spin-orbital degeneracy N . Analysis with the most divergent terms in the expansion shows that exponents of spectra of the slave boson and the pseudo-fermion in the M -channel model with 1 ≤ M ≪ N are given respectively by 1- n f 2 M / N and (2 n f - n f 2 ) M / N , where n f is the average number of localized electrons at the impurity site. When M =1, the results recover those obtained earlier in the single channel model. In the limits, n f →1 and M -2 ≪1, these results tend to those obtained by the non-crossing approximation (NCA) study. It also shows that the scattering rate of the conduction electrons in the M -channel model includes infrared divergent terms proportional to (1- n f )(1- M -2 ) in contrast to the absence of infrared divergent terms in the...

Spontaneous symmetry breaking of the light-front Gross-Neveu model is studied in the framework of the discretized light-cone quantization. Introducing a scalar auxiliary field and adding its kinetic term, we obtain a constraint on the longitudinal zero mode of the scalar field. This zero-mode constraint is solved by using the $1/N$ expansion. In the leading order, we find a nontrivial solution which gives the fermion nonzero mass and thus breaks the discrete symmetry of the model. It is essential for obtaining the nontrivial solution to treat adequately an infrared divergence which appears in the continuum limit. We also discuss the constituent picture of the model. The Fock vacuum is trivial and an eigenstate of the light-cone Hamiltonian. In the large $N$ limit, the Hamiltonian consists of the kinetic term of the fermion with dressed mass and the interaction term of these fermions., 25 pages, Latex, no figures, to be published in Progress of Theoretical Physics

The problem of determining the upper bounds for the ensemble-averaged reaction front position and speed in a fully developed three-dimensional turbulent flow has been examined, in which the reaction is of Kolmogorov-Petrovskii-Piskunov type and turbulent velocity is a Gaussian random field exhibiting long-range correlations and infrared divergence in the limit of large Reynolds number. An asymptotic method has been developed that gives the general formalism for determining the upper bounds for reaction front in the long-time, large-distance limit. Two anomalous scaling regimes and corresponding scaling functions have been determined by the use of exact renormalization procedure.

We investigate nonperturbative infrared effects for the O(N) linear sigma model in de Sitter space using the two-particle irreducible effective action at the Hartree truncation level. This approximation resums the infinite series of so-called superdaisy diagrams. For the proper treatment of ultraviolet divergences, we first study the renormalization of this approximation on a general curved background. Then, we calculate radiatively corrected masses and the effective potential. As a result, spontaneous symmetry breaking is possible, on the other hand, the Goldstone modes acquire a positive definite mass term due to the screening effects of interaction. Possible infrared divergence is self-regulated by the mass term. Furthermore, there is a symmetry restoring phase transition as a function of the Hubble parameter. In our approximation, the phase transition is of first order., Comment: 24 pages, 7 figures

Consistent factorization theorems in high-energy scattering near the threshold are presented in the framework of the soft-collinear effective theory. Traditional factorization theorem separates the soft and collinear parts successfully, but a final step should be supplemented if each part encounters infrared divergence. We present factorization theorems in which the infrared divergences appear only in the parton distribution functions and the infrared divergence is removed by carefully separating and reorganizing collinear and soft parts. The underlying physical idea is to isolate and remove the soft contributions systematically from the collinear part in loop corrections order by order. After this procedure, each factorized term in the scattering cross sections is free of infrared divergence, and can be safely computed using perturbation theory. This factorization procedure can be applied to various high-energy scattering processes. We show factorization theorems in Drell-Yan processes, deep inelastic scattering and Higgs production near the endpoint., Comment: 36 pages, 4 figures. To be published in JHEP

Schwinger-Dyson equations are used to study the phase diagram of QED in three dimensions. This computation is made with full frequency-dependence in the two-point function gap equations for the first time. We also demonstrate that reliable results are attainable in spite of an infrared divergence that is endemic to the theory. A theoretically sound method for dealing with cutoff ultraviolet regulators is presented. Finally, it is shown that the quenched and instantaneous approximations often used in the literature are inaccurate., 12 pages, 8 figures

An analytic ground state is proposed for the unbiased spin-boson Hamiltonian, which is non-Gaussian and beyond the Silbey-Harris ground state with lower ground state energy. The infrared catastrophe in Ohmic and sub-Ohmic bosonic bath plays an important role in determining the degeneracy of the ground state. We show that the infrared divergence associated with the displacement of the nonadiabatic modes in bath may be removed from the proposed ground state for the coupling $\alpha, Comment: 11 pages, 2 figures

It is generally believed that the BCS-BEC evolution in fermionic systems with $s$-wave pairing is a smooth crossover. However, for nonzero orbital-angular-momentum pairing such as $p$- or $d$-wave pairing, the system undergoes a quantum phase transition at the point where the chemical potential $\ensuremath{\mu}$ vanishes. In this paper, we study the BCS-BEC quantum phase transition and the collective excitations associated with the order-parameter fluctuations in two-dimensional fermionic systems with $p$- and $d$-wave pairings. We show that the quantum phase transition in such systems can be generically traced back to the infrared behavior of the fermionic excitation at $\ensuremath{\mu}=0$: ${E}_{\mathbf{k}}\ensuremath{\sim}{k}^{l}$, where $l=1,2$ is the quantum number of the orbital angular momentum. The nonanalyticity of the thermodynamic quantities is due to the infrared divergence caused by the fermionic excitation at $\ensuremath{\mu}=0$. As a result, the evolution of the Anderson-Bogoliubov mode is not smooth: Its velocity is nonanalytical across the quantum phase transition.

We propose new dynamical equations to describe fully developed turbulence. We begin with the Wyld equations (WE), which are exact solutions of the NSE. The WE, and their Langevin‐like representation, show that nonlinearities induce a turbulent force ft(k) and a turbulent viscosity νt(k), which are given by an infinite series of Wyld diagrams. The series for νt(k) is renormalizable, and its sum can be found using RNG methods. The result, Eq. (2a), holds for stirring forces fext with an arbitrary correlation function φ and generalizes previous RNG results, which neglected ft and were limited to power law φ∼k1−2e. To recover Kolmogorov law, these earlier RNG‐based theories were forced to introduce an ad hoc stirring force with a prescribed φ∼k−3. By contrast, we show that ∼k−3 belongs to φ, which is the correlation function of ft, and that in the inertial range ft≫fext. The series for φ cannot be summed because of a nonrenormalizable infrared divergence (IR) with an infinite number of divergent irreducible...

We calculate hadronic screening masses in the vector channel mode by using the QCD sum rule. We focus on the effect of the O(αs) correction to the Wilson coefficient of the identity operator. It is shown that the O(αs) correction cancels the effect of the gluon condensate and gives favorable results. It implies that the screening mass close to 2πT in the vector mode is no evidence for the existence of free quarks and gluons and that it results from the sum of all the perturbative and nonperturbative effects. We also show that the infrared divergence in three dimensional QCD, which is brought about by dimensional reduction, cancels each other and does not appear in the final results.

The dynamics of massive particles in the collinear high momentum regime is investigated. Methods hitherto exploiting large time asymptotic Hamiltonians in the Dirac picture for the treatment of infrared divergences are adapted to the collinear asymptotic dynamics. The essential role of time ordering of the dressing operators is brought out.

We reassess the validity of the current-algebra based low-energy theorem of pion photoproduction on the nucleon using the Skyrme model. We find that one of the off-shell electromagnetic form factors of the nucleon exhibits infrared divergence in the chiral limit. This contribution introduces an additional term to the threshold amplitude predicted by the low-energy theorem. The emergence of the additional term indicates an unavoidable necessity of off-shell form factors in deriving the low-energy theorem. In the case of neutral pion production, the new contribution to the threshold amplitude is found to be comparable in magnitude to the low-energy theorem's prediction and has the opposite sign. In the charged pion production channels, the correction to the theorem is shown to be relatively small.

The large-scale dynamics of a reaction front in a turbulent flow in the limit of large Reynolds number has been studied starting from the Kolmogorov-Petrovskii-Piskunov equation, modified by the random convection term. Random velocity has been assumed to be a homogeneous Gaussian field with Kolmogorov energy spectrum and infrared divergence. An upper bound for the position and speed of the reaction front in the long-time, large-distance limit has been derived by the method of random characteristics and a renormalization procedure. It has been shown that the infrared divergence of the random velocity field leads to the acceleration of a coarse-grained reaction front.

Based on the two-level model and the unified theory of low frequency relaxation processes for condensed matter, we studied the magnetic after-effect spectrum in the temperature range between 250 and 350 K for the amorphous Fe50Ni30B20 alloy after an annealing treatment for 2 h at 480 K. The calculated infrared infrared divergence exponent n = 0.11, and the characteristic relaxation time τ∞ = 2.8 × 10−17 s. The apparent activation energy EA obtained at the temperature of the relaxation peak is about 1.7 eV. These values are in good agreement with experiments. The calculations indicate that for this amorphous alloy, the magnetic after effects are caused by local rearrangement of atom pairs FeB and NiB caused by jumps of B atoms.

In the framework of Anisotropic Chromodynamics, a non-perturbative realization of QCD, we develop the Low-Nussinov picture of the Pomeron. In this approach all the usual problems of low pT perturbative calculations (infrared divergence) are naturally absent. Thus, we are able to perform an ab initio calculation of the hadron-hadron total cross section. The result is a cross section of the same magnitude as indicated experimentally and approximately energy-independent (with a log^2 s growth). We further discuss the pT dependence of the hadron-hadron elastic-scattering cross section, which displays all the experimentally observed features., Comment: 8 pages (LaTeX, plus 4 postscript figures in a separate file), report number MITH 94/13 *** Replaced figures file with uuencoded, compressed, tarred version ***

Application of Krein space quantization to the linear gravity in de Sitter space-time have constructed on Gupta-Bleuler vacuum state, resulting in removal of infrared divergence and preserving de Sitter covariant. By pursuing this path, the non uniqueness of vacuum expectation value of the product of field operators in curved space-time disappears as well. Then the vacuum expectation value of the product of field operators can be defined properly and uniquely., 19 pages, typos corrected, reference addeded, further comments add

Let us investigate in more detail the origin of the logarithmic term that we found in the previous chapter. We examine the s–d Hamiltonian from this point of view. We first consider the two total wavefunctions of conduction electrons moving in two different local potentials. The overlap integral and matrix elements of these two wavefunctions contain logarithmic terms. In particular, the overlap integral vanishes at zero temperature in general. Second, we investigate the development of the wavefunction under a time-dependent perturbation where one potential changes into the other one abruptly at a particular time. This problem is closely related to the physics of the s-d interaction, since the potential changes quite abruptly as the spin-flips occur due to the s-d interaction. This problem is solved using the Nozieres-de Dominicis method, and we apply these general considerations to the s–d Hamiltonian to obtain the perturbation expansion of the partition function and other physical quantities. The behavior of the localized spin at low temperatures is clarified using the scaling method applied to the s–d Hamiltonian. The Anderson orthogonality theorem This section is based mainly on Anderson (1967a,b). In the previous chapter, we showed that the logarithmic singularity arises as a function of temperature in several physical quantities for systems governed by the s–d Hamiltonian due to flips of the localized spin. It is essential in this phenomenon that the localized spin has an internal degree of freedom.

In a previous paper [1], we studied the $\eta'$ mass and formulated its chirally symmetric coupling to fermions which induces electric dipole moment (EDM). Here we calculate the EDM to one-loop. It is finite, having no ultraviolet divergence while its infrared divergence is canceled by soft photon emission processes \emph{exactly} as for $\theta=0$. The coupling does not lead to new divergences (not present for $\sin\theta=0$) in soft photon processes either. Furthermore, as it was argued previously [1], the EDM vanishes if suitable mixed quantum states are used. This means that in a quantum theory based on such mixed states, a strong bound on EDM will not necessarily lead to a strong bound such as $|\sin \theta|\lesssim 10^{-11}$ . This fact eliminates the need to fine-tune $\theta$ or for the axion field., Comment: 16 pages, 1 figure

We explore the spin-boson model in a special case, i.e., with zero local field. In contrast to previous studies, we find no possibility for quantum phase transition (QPT) happening between the localized and delocalized phases, and the behavior of the model can be fully characterized by the even or odd parity as well as the parity breaking, instead of the QPT, owned by the ground state of the system. Our analytical treatment about the eigensolution of the ground state of the model presents for the first time a rigorous proof of no-degeneracy for the ground state of the model, which is independent of the bath type, the degrees of freedom of the bath and the calculation precision. We argue that the QPT mentioned previously appears due to unreasonable treatment of the ground state of the model or of the infrared divergence existing in the spectral functions for Ohmic and sub-Ohmic dissipations., 5 pages, 1 figure. Comments are welcome

We compute the analogue Hawking radiation for modes which posses a small wave vector perpendicular to the horizon. For low frequencies, the resulting mass term induces a total reflection. This generates an extra mode mixing that occurs in the supersonic region, which cancels out the infrared divergence of the near horizon spectrum. As a result, the amplitude of the undulation (0-frequency wave with macroscopic amplitude) emitted in white hole flows now saturates at the linear level, unlike what was recently found in the massless case. In addition, we point out that the mass introduces a new type of undulation which is produced in black hole flows, and which is well described in the hydrodynamical regime., 37 pages, 8 figures, published version

We estimate fermion loop corrections to the two-point correlation function of primordial tensor perturbations in a slow-roll inflationary background. We particularly compute an explicit term of one-loop correction from a massless fermion, and then extend to the complete Interaction Hamiltonian. After that, we study one-loop corrections contributed by a massive fermion to primordial tensor fluctuations. The loop correction arisen from a massless fermion field contains logarithms and thus may constrain the validity of perturbation theory in inflationary cosmology, but the situation could be relaxed once the fermion's mass is taken into account. Another one-loop diagram for a massive fermion which involves one vertex is constrained by a UV cutoff as expected by quantum field theory. Our result shows that loop corrections of a fermion field have the same sign as those of a scalar field, and thus implies that the inclusion of fermion loop corrections may not help to alleviate the issue of IR divergence in inflationary cosmology., Comment: 12 pages

The physics of the pseudogap state is intimately linked with the pairing mechanism that gives rise to superfluidity in quantum gases and to superconductivity in high-Tc cuprates, and therefore, both in quantum gases and superconductors, the pseudogap state and preformed pairs have been under intensive experimental scrutiny. Here, we develop a path integral treatment that provides a divergence-free description of the paired state in two-dimensional Fermi gases. Within this formalism, we derive the pseudogap temperature and the pair fluctuation spectral function, and compare these results with the recent experimental measument of the pairing in the two-dimensional Fermi gas. The removal of the infrared divergence in the number equations is shown both numerically and analytically, through a study of the long-wavelength and low-energy limit of the pair fluctuation density. Besides the pseudogap temperature, also the pair formation temperature and the critical temperature for superfluidity are derived. The latter corresponds to the Berezinski-Kosterlitz-Thouless (BKT) temperature. The pseudogap temperature, which coincides with the pair formation temperature in mean field, is found to be suppressed with respect to the pair formation temperature by fluctuations. This suppression is strongest for large binding energies of the pairs. Finally, we investigate how the pair formation temperature, the pseudogap temperature and the BKT temperature behave as a function of both binding energy and imbalance between the pairing partners in the Fermi gas. This allows to set up phase diagrams for the two-dimensional Fermi gas, in which the superfluid phase, the phase-fluctuating quasicondensate, and the normal state can be identified., 17 pages, 6 figures

where 2L1 is the level spacing of two-state spin described by the Pauli matrix 6z and 6±=6x±i6y, w; is the excitation energy of boson with quantum number j, and v = 'LJ;(J..;/w;) · (bjb;). This is the unitary transformed version offamiliar H =-Ll· 6x +LJ;w;b;+b;+1/2·6z·'LJ;J..;(b;++b;)-LJ;J..]/4w; by unitary operator U=exp[6z·v/2]. The IS means that fi and H are invariant under inversion operation P( 6x, 6y, 6z, b;, bt)P-=(6x, -(Jy, -6z, -b;, -b;+), where P=exp[i7r'LJ;b/b;+i(.n/2)(6x-1)]. The spectral density of interaction is assumed to be 'LJ;J../8(w;-w)=2aw·(w/wcY-r Xexp[ -w/wc] where s>O and a is a dimensionless strength. Boson system fiB = 'LJ;w;b; + b; in (1) consists of bosons which displace themselves according to flips of spin. We assume that the boson system is thermodynamically large and white in the sense that cutoff wc')>Ll. We choose the eigenstates of 6z for those of spin. In previous worksl,ZJ the author proposed the concept of dynamic compensation, and predicted that the ground state (GS) in the white limit exhibits the transition at ac=1/2 from the delocalized (tunneling) one in a ac for s = 1, the localized one over the whole a except zero for s 1. The first two results of GS are due to the dynamic compensation of infrared divergence. There is no infrared divergence in s > 1 from the outset. This prediction is different from the paradigmatic description based on the static renormalization of infrared divergence.l,l In this paper we present the rigorous results of the two-branch structure of GS, excited state and their energies, thermodynamics and dynamics, restricting ourselves to the case s=1 in order to save space. The full details and other cases of s will be reported elsewhere.

A new algorithm is developed here for Monte Carlo simulation of turbulent diffusion with random velocity fields having a power law spatial spectrum, arbitrarily many statistical scales, long range correlations, and infrared divergence. This algorithm uses an expansion of the moving average representation of a Gaussian random field via a specific orthonormal basis which exploits the scaling behavior of the random field and yields a compact representation of the field despite infrared divergence. The orthonormal basis involves a family of wavelets due to Alpert and Rokhlin and the vanishing of a large number of moments for this basis (order 3 or 4) is crucial for compact representation of the statistical velocity field. The authors also develop a rigorous practical a priori energy criterion for truncation of the wavelet expansion; furthermore, for moment cancellations with orders 3 or 4 and a fixed energy tolerance, the number of Gaussian random basis elements needed by the method is sublinear in the exponent m, where 1 < |x| < 2m denotes the range of active velocity scales. The algorithm developed here has remarkably low variance as regards sampling errors. For example, for the infrared divergent velocity spectrum corresponding to the Kolmogoroff spectrum in an exactly solvable model, the velocity structure function is simulated accurately for separation distances over more than five decades with only 792 random basis elements and 100 ensemble realizations; with this same singular spectrum in the model problem, the pair dispersion statistic for the passive scalar can be determined within errors of 3% throughout over five decades of pair separation distance with only 792 random elements, 1000 realizations, and a few hours calculation on a workstation. All of the computational algorithms and results are presented for a nontrivial exactly solvable model and are described within a mathematical framework of error analysis where analytic, sampling, and discretization errors are treated separately.