HEAT-KERNEL EXPANSION AT FINITE TEMPERATURE

We show how the zero-temperature result for the heat-kernel asymptotic expansion can be generalized to the finite-temperature one. We observe that this general result depends on the interesting ratio square-root tau/beta, where tau is the regularization parameter and beta = 1/T, so that the zero-temperature limit beta --> infinity corresponds to the cutoff limit tau --> 0. As an example, we discuss some aspects of the axial model at finite temperature.

ANOMALIES IN CURVED SPACETIME AT FINITE TEMPERATURE

We discuss the problem of the breakdown of conformal and gauge symmetries at finite temperature in curved-spacetime background, when the changes in the background are gradual, in order to have a well-defined quantum field theory at finite temperature. We obtain the expressions for Seeley's coefficients and the heat-kernel expansion in this regime. As applications, we consider the self-interacting lambdaphi4 and chiral Schwinger models in curved backgrounds at finite temperature.

CHIRAL SCHWINGER MODEL WITH A PODOLSKY TERM AT FINITE-TEMPERATURE

We study an exactly solvable two-dimensional model which mimics the basic features of the standard model. This model combines chiral coupling with an infrared behavior which resembles low energy QCD. This is done by adding a Podolsky higher-order derivative term in the gauge field to the Lagrangian of the usual chiral Schwinger model. We adopt a finite temperature regularization procedure in order to calculate the non-trivial fermionic Jacobian and obtain the photon and fermion propagators, first at zero temperature and then at finite temperature in the imaginary and real time formalisms. Both singular and non-singular cases, corresponding to the choice of the regularization parameter, are treated. In the nonsingular case there is a tachyonic mode as usual in a higher order derivative theory, however in the singular case there is no tachyonic excitation in the spectrum.

Virial coefficients from (2+1)-dimensional QED effective actions at finite temperature and density

From spinor and scalar (2 + 1)-dimensional QED effective actions at finite temperature and density in a constant magnetic field background, we calculate the corresponding virial coefficients for particles in the lowest Landau level. These coefficients depend on a parameter theta related to the time-component of the gauge field, which plays an essential role for large gauge invariance. The variation of the parameter theta might lead to an interpolation between fermionic and bosonic virial coefficients, although these coefficients are singular for theta = pi/2.

Three-dimensional finite element analysis of MHD duct flow by the penalty function formulation

A numerical scheme based on the Finite Element Method (FEM) is presented to calculate the full solution of a three-dimensional steady magnetohydrodynamic (MHD) flow with moderately high Hartmann numbers and interaction parameters. An incompressible, viscous and electrically conducting liquid-metal is considered. Assuming a low magnetic Reynolds number, the solution method solves the coupled Navier-Stokes and Maxwell's equations through the use of a penalty function method. Results are presented for Hartmann numbers in the range 10(2)-10(3).

An extended Weyl-Wigner transformation for special finite spaces

We extend the Weyl-Wigner transformation to those particular degrees of freedom described by a finite number of states using a technique of constructing operator bases developed by Schwinger. Discrete transformation kernels are presented instead of continuous coordinate-momentum pair system and systems such as the one-dimensional canonical continuous coordinate-momentum pair system and the two-dimensional rotation system are described by special limits. Expressions are explicitly given for the spin one-half case. © 1988.

Infrared finite gluon propagator and the structure of chiral symmetry breaking

We study the chiral symmetry breaking in QCD, using an effective potential for composite operators, with infrared finite gluon propagators that have been found by numerical calculation of the Schwinger-Dyson equations as well as in lattice simulations. The existence of a gluon propagator that is finite at k2 = 0 modifies substantially the transition between the phases with and without chiral symmetry.

Critical coupling for dynamical chiral-symmetry breaking with an infrared finite gluon propagator

We compute the critical coupling constant for the dynamical chiral-symmetry breaking in a model of quantum chromodynamics, solving numerically the quark self-energy using infrared finite gluon propagators found as solutions of the Schwinger-Dyson equation for the gluon, and one gluon propagator determined in numerical lattice simulations. The gluon mass scale screens the force responsible for the chiral breaking, and the transition occurs only for a larger critical coupling constant than the one obtained with the perturbative propagator. The critical coupling shows a great sensibility to the gluon mass scale variation, as well as to the functional form of the gluon propagator.

Infrared finite solutions for the gluon propagator and the QCD vacuum energy

Nonperturbative infrared finite solutions for the gluon polarization tensor have been found, and the possibility that gluons may have a dynamically generated mass is supported by recent Monte Carlo simulation on the lattice. These solutions differ among themselves, due to different approximations performed when solving the Schwinger-Dyson equations for the gluon polarization tensor. Only approximations that minimize energy are meaningful, and, according to this, we compute an effective potential for composite operators as a function of these solutions in order to distinguish which one is selected by the vacuum. © 1997 Elsevier Science B.V.

Q-deformed fermionic Lipkin model at finite temperature

The interplay between temperature and q-deformation in the phase transition properties of many-body systems is studied in the particular framework of the collective q-deformed fermionic Lipkin model. It is shown that in phase transitions occuring in many-fermion systems described by su(2)q-like models are strongly influenced by the q-deformation.

Closed expressions for Lie algebra invariants and finite transformations

A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements requires the use of projectors, whose coefficients are invariant polynomials. The detailed general forms of these projectors are given. Closed expressions for finite Lorentz transformations, both homogeneous and inhomogeneous, as well as for Galilei transformations, are found as examples.

Pre-weighted homogeneous map germs finite determinacy and topological triviality

In this paper we introduce the notion of G-pre-weighted homogeneous map germ, (G is one of Mather's groups A or K.) and show that any G-pre-weighted homogeneous map germ is G-finitely determined. We also give an explicit order, based on the Newton polyhedron of a pre-weighted homogeneous germ of function, such that the topological structure is preserved after perturbations by terms of higher order.

Construction and decoding of BCH codes over finite commutative rings

BCH codes over arbitrary finite commutative rings with identity are derived in terms of their locator vector. The derivation is based on the factorization of xs -1 over the unit ring of an appropriate extension of the finite ring. We present an efficient decoding procedure, based on the modified Berlekamp-Massey algorithm, for these codes. The code construction and the decoding procedures are very similar to the BCH codes over finite integer rings. © 1999 Elsevier B.V. All rights reserved.