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

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.

11 pages, latex, 5 figures (one correction and one new reference)

References in corpus (1)

• Free Variables and the Two Matrix Model

Cited by in corpus (4)

• The Master Field for QCD and $q$-Deformed Quantum Field Theory
• The Master Field for Large $N$ Matrix Models and Quantum Groups
• Large $N$ Solution of the 2D Supersymmetric Yang-Mills Theory
• Large $N$ Matrix Models and $q$-Deformed Quantum Field Theories