SUPERSYMMETRIC EXTENSION OF MOYAL ALGEBRA AND ITS APPLICATION TO THE MATRIX MODEL

We construct operator representation of Moyal algebra in the presence of fermionic fields. The result is used to describe the matrix model in Moyal formalism that treat gauge degrees of freedom and outer degrees of freedom equally.

SPIN TOPOLOGICAL QUANTUM FIELD THEORIES

Starting from the quantum group [Formula: see text], we construct operator invariants of 3-cobordisms with spin structure, satisfying the requirements of a topological quantum field theory and refining the Reshetikhin–Turaev and Turaev–Viro models. We establish the relationship between these two refined theories.