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

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.

More comments about a new gauge theory and more references are added, 14 pages, latex

References in corpus (5)

• Mastering the Master Field
• Free Variables and the Two Matrix Model
• The Master Field for Large $N$ Matrix Models and Quantum Groups
• Non--Commutative (Quantum) Probability, Master Fields and Stochastic Bosonization
• The Master Field for Rainbow Diagrams and Free Non-Commutative Random Variables

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