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

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 spacetime and to use the Wightman correlation functions. The BRST quantization of the master field for gauge theory and a loop equation are considered. e-mail: [email protected] e-mail: [email protected]