Large $N$ QCD and $q$-Deformed Quantum Field Theories

Abstract

A construction of master field describing multicolour QCD is presented. The master fields for large N matrix theories satisfy to standard equations of relativistic field theory but fields are quantized according $q$-deformed commutation relations with $q=0$. These commutation relations are realized 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 and BRST-invariance.

4 pages, latex.Invited talk at the Second International Sakharov Conference on Physics, Moscow, May 1996