Integration Over a Generic Algebra

Abstract

In this paper we consider the problem of quantizing theories defined over configuration spaces described by noncommuting parameters. If one tries to do that by generalizing the path-integral formalism, the first problem one has to deal with is the definition of integral over these generalized configuration spaces. This is the problem we state and solve in the present work, by constructing an explicit algorithm for the integration over a generic algebra. The general conditions a given algebra has to satisfy in order to admit our integration are not yet fully understood, but many examples are discussed in order to illustrate our construction.