The Master Field for Rainbow Diagrams and Free Non-Commutative Random Variables

TL;DR

This paper introduces an explicit representation of the master field for rainbow diagrams in large N theories using noncommutative random variables within a modified interaction framework, advancing understanding of planar diagram structures.

Contribution

It provides a novel explicit construction of the master field for rainbow diagrams employing noncommutative variables in a modified Fock space setting, differing from traditional approaches.

Findings

Explicit master field representation derived

Use of rational functions in the modified interaction framework

Enhanced understanding of rainbow diagram structures

Abstract

The master field for a subclass of planar diagrams, so called rainbow diagrams, for higher dimensional large N theories is considered. An explicit representation for the master field in terms of noncommutative random variables in the modified interaction representation in the Boltzmannian Fock space is given. A natural interaction in the Boltzmannian Fock space is formulated by means of a rational function of the interaction Lagrangian instead of the ordinary exponential function in the standard Fock space.