Light-front field theories at finite temperature

Abstract

We study the question of generalizing light-front field theories to finite temperature. We show that the naive generalization has serious problems and we identify the source of the difficulty. We provide a proper generalization of these theories to finite temperature based on a relativistic description of thermal field theories, both in the real and the imaginary time formalisms. Various issues associated with scalar and fermion theories, such as non-analyticity of self-energy, tensor decomposition are discussed in detail.

Unruh effect in the general light-front frame

“…It is interesting to study the phenomenon of Unruh effect within the context of quantum field theories quantized on the light-front (equalt) in GLF [6] for the following reasons. Since the statistical density matrix in light-front field theories does not correspond to a naive generalization of the known density matrix [3,4,5], further support for the structure of this density matrix in GLF can be obtained from studying the thermal behavior of the vacuum in an accelerated coordinate system. This, of course, immediately raises this interesting issue, namely, since the form of the line element in (3) shows that there are now two distinct possibilities for acceleration (unlike the Minkowski frame), it is not a priori clear whether this would lead to two distinct temperatures for the Unruh effect (corresponding to the two directions for acceleration) and how this will be compatible with the unique temperature of the GLF description following from Tolman's law in (4).…”

“…It has been observed in recent years that a statistical description of theories quantized on the light-front [1,2] prefers a general coordinate frame [3,4,5]. Denoting the Minkowski coordinates by x µ = (t, x, y, z) and the coordinates of the general light-front frame byx µ = (t,x,ȳ,z), the relation between the two can be written as [6] t = t + z,z = At + Bz, x = x,ȳ = y,…”

“…(1) represents the conventional light-front frame (CLF) while for A = 0, B = 1 we have the oblique light-front frame (OLF) where most of the discussions of statistical mechanics have been carried out thus far [3,4,5,7,8]. In general, if a quantum field theory quantized at equal time t is at temperature T M in the Minkowski space, then by Tolman's law [9], the corresponding temperature for the theory quantized at equalt in the generalized light-front frame is given by…”

Spectrum and thermodynamic properties of two-dimensionalN=(1,1)super Yang-Mills theory with fundamental matter and a Chern-Simons term

“…However, as discussed in Refs. [9,10], the above prescription leads to singular results for well-known quantities which are finite in the equal-time approach. Their argument is based on the fact that using e ÿ LC p ÿ as the partition function implies that the physical system is in contact with a heat bath that has been boosted to the lightcone frame.…”

Light-Front Quantization and QCD Phenomena

“…Light-front quantization can also be used to obtain a frame-independent formulation of thermodynamics systems, such as the light-front partition function [4,5,6,7,8,9,10]. This application is particularly useful for relativistic systems, such as the hadronic system produced in the central rapidity region of high energy heavy-ion collisions.…”