Title
Spherical harmonics and integration in superspace : 2 Spherical harmonics and integration in superspace : 2
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
London ,
Subject
Physics
Source (journal)
Journal of physics : A : mathematical and theoretical / Institute of Physics. - London
Volume/pages
42(2009) :24 , p. 245204,1-245204,18
ISSN
1751-8113
1751-8121
Article Reference
245204
Carrier
E-only publicatie
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
The study of spherical harmonics in superspace, introduced in (De Bie and Sommen 2007 J. Phys. A: Math. Theor. 40 7193) is further elaborated. A detailed description of spherical harmonics of degree k is given in terms of bosonic and fermionic pieces, which also determines the irreducible pieces under the action of SO(m) x Sp(2n). In the second part of the paper, this decomposition is used to describe all possible integrations over the supersphere. It is then shown that only one possibility yields the orthogonality of spherical harmonics of different degrees. This is the so-called Pizzetti-integral of which it was shown in (De Bie and Sommen 2007 J. Phys. A: Math. Theor. 40 7193) that it leads to the Berezin integral.
E-info
https://repository.uantwerpen.be/docman/iruaauth/305534/e131316.pdf
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