Hermite and Gegenbauer polynomials in superspace using Clifford analysis

Details Hermite and Gegenbauer polynomials in superspace using Clifford analysis Hermite and Gegenbauer polynomials in superspace using Clifford analysis

2007-07-19

arxiv.org/abs/0707.2863v1

J.Phys.A40:10441-10456,2007

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, accepted for publication in J. Phys. A

Scientific paper

10.1088/1751-8113/40/34/004

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.

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