The Master Field for QCD and $q$-Deformed Quantum Field Theory

TL;DR

This paper constructs master fields for large N matrix models and gauge theories using a novel quantization rule with Boltzmannian Fock space, revealing new structures in quantum field theory.

Contribution

It introduces a new approach to define master fields in large N gauge theories using Boltzmannian quantization and explores their properties and symmetries.

Findings

Master fields satisfy standard relativistic equations.

Fields are quantized with a new Boltzmannian rule.

The approach works in Minkowski space-time with Wightman functions.

Abstract

The master fields for the large $N$ limit of matrix models and gauge theory are constructed. The master fields satisfy to standard equations of relativistic field theory but fields are quantized according to a new rule. To define the master field we use the Yang-Feldman equation with a free field quantized in the Boltzmannian Fock space. The master field for gauge theory does not take values in a finite-dimensional Lie algebra however there is a non-Abelian gauge symmetry. For the construction of the master field it is essential to work in Minkowski space-time and to use the Wightman correlation functions. The BRST quantization of the master field for gauge theory and a loop equation are considered.