2009/05/13 by Hendrik De Bie, De Bie, H., David Eelbode +3
Mathematics · Physics and Astronomy · #30G35 #58C50 #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.0905.2092
openalex publication_date 2009/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The study of spherical harmonics in superspace, introduced in [J. Phys. A: Math. Theor. 40 (2007) 7193-7212], 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 degree. This is the so-called Pizzetti-integral of which it was shown in [J. Phys. A: Math. Theor. 40 (2007) 7193-7212] that it leads to the Berezin integral.