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Teoreticheskaya i Matematicheskaya Fizika, 1984, Volume 58, Number 2, Pages 229–232
(Mi tmf4330)
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This article is cited in 7 scientific papers (total in 7 papers)
Clifford algebras as superalgebras and quantization
D. A. Leites
Abstract:
On supermanifolds there are two types of mechanics, to which there
correspond superalgebras of functions with Poisson or Butan
brackets (respectively, antibrackets). For them, quantizations are
constructed in the following senses: 1) representations of the
commutation relations, 2) deformation of the Poisson
(respectively, Butan) superalgebra into the Lie superalgebra of
differential operators, 3) analogs of the spinor representation of
a symplectic (orthogonal) Lie algebra. The Clifford algebra is
given a new interpretation. Invariant polynomials and Casimir
operators on the Poisson superalgebra are described.
Received: 18.08.1982
Citation:
D. A. Leites, “Clifford algebras as superalgebras and quantization”, TMF, 58:2 (1984), 229–232; Theoret. and Math. Phys., 58:2 (1984), 150–152
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https://www.mathnet.ru/eng/tmf4330 https://www.mathnet.ru/eng/tmf/v58/i2/p229
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Abstract page: | 472 | Full-text PDF : | 191 | References: | 56 | First page: | 2 |
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