Integration over a generic algebra
Mathematical Physics
2009-10-30 v2 High Energy Physics - Theory
math.MP
Abstract
In this paper we consider the problem of quantizing theories defined over configuration spaces described by non-commuting 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 general algebra. Many examples are discussed in order to illustrate our construction.
Cite
@article{arxiv.physics/9702019,
title = {Integration over a generic algebra},
author = {R. Casalbuoni},
journal= {arXiv preprint arXiv:physics/9702019},
year = {2009}
}
Comments
31 pages, Latex. A few typos have been corrected. Some comments about algebras with identity and about inner derivations have been inserted, together with a further example: the q-bosonic oscillator