INTEGRATION OVER A GENERIC ALGEBRA

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