Finite-temperature field theory on the light front

TL;DR

This paper develops a finite-temperature light-front quantum field theory, especially for QCD, enabling a new approach to relativistic statistical systems like heavy ion collisions, with advantages in defining Green's functions and parton densities.

Contribution

It introduces a comprehensive formulation of finite-temperature light-front field theory, addressing zero-mode issues and connecting Green's functions to parton distributions in a novel way.

Findings

Green's functions are defined with 2-component spinors avoiding doublers.

The theory provides a new framework for relativistic statistical systems.

Parton densities are interpreted as light-front density matrices.

Abstract

The formulation of statistical physics using light-front quantization, instead of conventional equal-time boundary conditions, has important advantages for describing relativistic statistical systems, such as heavy ion collisions. We develop light-front field theory at finite temperature and density with special attention to quantum chromodynamics. First, we construct the most general form of the statistical operator allowed by the Poincare algebra. In light-front quantization, the Green's functions of a quark in a medium can be defined in terms of just 2-component spinors and does not lead to doublers in the transverse directions. Since the theory is non-local along the light cone, we use causality arguments to construct a solution to the related zero-mode problem. A seminal property of light-front Green's functions is that they are related to parton densities in coordinate space. Namely, the diagonal and off-diagonal parton distributions measured in hard scattering experiments can be interpreted as light-front density matrices.