Hermite and Gegenbauer polynomials in superspace using Clifford analysis
High Energy Physics - Theory
2008-11-26 v1 Classical Analysis and ODEs
Abstract
The Clifford-Hermite and the Clifford-Gegenbauer polynomials of standard Clifford analysis are generalized to the new framework of Clifford analysis in superspace in a merely symbolic way. This means that one does not a priori need an integration theory in superspace. Furthermore a lot of basic properties, such as orthogonality relations, differential equations and recursion formulae are proven. Finally, an interesting physical application of the super Clifford-Hermite polynomials is discussed, thus giving an interpretation to the super-dimension.
Cite
@article{arxiv.0707.2863,
title = {Hermite and Gegenbauer polynomials in superspace using Clifford analysis},
author = {Hendrik De Bie and Frank Sommen},
journal= {arXiv preprint arXiv:0707.2863},
year = {2008}
}
Comments
18 pages, accepted for publication in J. Phys. A