TY - JOUR UR - http://lib.ugent.be/catalog/pug01:920682 ID - pug01:920682 LA - eng TI - Spherical harmonics and integration in superspace II PY - 2009 JO - (2009) JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL SN - 1751-8113 PB - 2009 AU - De Bie, Hendrik TW16 002000066440 AU - Eelbode, David TW16 801001561555 052194312997 AU - Sommen, Franciscus AB - 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. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 920682 | ||
005 | 20161219154520.0 | ||
008 | 100402s2009------------------------eng-- | ||
022 | a 1751-8113 | ||
024 | a 000266457600008 2 wos | ||
024 | a 1854/LU-920682 2 handle | ||
024 | a 10.1088/1751-8113/42/24/245204 2 doi | ||
040 | a UGent | ||
245 | a Spherical harmonics and integration in superspace II | ||
260 | c 2009 | ||
520 | a 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. | ||
598 | a A1 | ||
100 | a De Bie, Hendrik u TW16 0 002000066440 0 801002044535 | ||
700 | a Eelbode, David u TW16 0 801001561555 0 052194312997 0 001997397324 | ||
700 | a Sommen, Franciscus u TW16 0 801000476064 | ||
650 | a Physics and Astronomy | ||
653 | a CLIFFORD ANALYSIS | ||
773 | t JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL g J. Phys. A-Math. Theor. 2009. 42 (24) q 42:24< | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/920682/file/931617 z [ugent] y DeBie_2009_JPA_42_24_a245204.pdf | ||
920 | a article | ||
852 | x EA b TW16 | ||
922 | a UGENT-EA |
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