Notes on Weyl-Clifford algebras

Abstract

Here is discussed generalization of Clifford algebras, l^n-dimensional Weyl-Clifford algebras T(n,l) with n generators t_k satisfying equation $({\sum }_{k=1}^n{a}_k{t}_k{)}^l={\sum }_{k=1}^n{a}_k^l$. It is originated from two basic and well known constructions: representation of Clifford algebras via tensor products of Pauli matrices together with extension for l > 2 using Weyl commutation relations. Presentation of such general topics here may not pretend to entire originality or completeness and it is rather a preliminary excursus into this very broad and interesting area of research.

17 pages, 10pt LaTeXe; v2 corrected disappointing typos (swap p,q)