Pseudodifferential Operators in Superanalysis

Abstract

In this chapter we expose the theory of PDO on a superspace over topological CSM. These superspaces can have a finite as well as infinite number of supercoordinates. Thus, the proposed PDO calculus serves as a mathematical basis for the quantization of physical supersystems with a finite as well as infinite number degrees of freedom. In a finite-dimensional case, we obtain quantum mechanics on the superspace R^n,mΛ and in an infinite-dimensional case we obtain a quantum theory of a superfield, in particular, that of a superstring and superstring field, and fermion theories and boson theories with anticommuting Faddeev-Popov ghosts.