Large $N$ Matrix Models and $q$-Deformed Quantum Field Theories

Abstract

Recently it was shown that an asymptotic behaviour of $SU(N)$ gauge theory for large $N$ is described by q-deformed quantum field. The master fields for large N theories satisfy to standard equations of relativistic field theory but fields satisfy $q$-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. The gauge master field for a subclass of planar diagrams, so called half-planar diagrams, is also considered. A recursive set of master fields summing up a matreoshka of 2-particles reducible planar diagrams is briefly described.

17 pages, latex. To appear in "From Field Theory to Quantum Groups", World Scientific. Proceedings to honor J.Lukierski in his 60th birthday

References in corpus (1)

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