Title 



Spherical harmonics and integration in superspace : 2


Author 





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 socalled Pizzettiintegral 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.  

Language 



English


Source (journal) 



Journal of physics : A : mathematical and theoretical / Institute of Physics.  London 

Publication 



London : 2009


ISSN 



17518113 [print]
17518121 [online]


Volume/pages 



42:24(2009), p. 245204,1245204,18


Article Reference 



245204


ISI 



000266457600008


Medium 



Eonly publicatie


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