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This article is cited in 30 scientific papers (total in 30 papers)
How to Quantize the Antibracket
D. A. Leitesa, I. M. Shchepochkinab a Stockholm University
b Independent University of Moscow
Abstract:
We show that in contrast to $\mathfrak{po}(2n|m)$, its quotient modulo center, the Lie superalgebra $\mathfrak{h}(2n|m)$ of Hamiltonian vector fields with polynomial coefficients, has exceptional additional deformations for $(2n|m)=(2|2)$ and only for this superdimension. We relate this result to the complete description of deformations of the antibracket (also called the Schouten or Buttin bracket). It turns out that the space in which the deformed Lie algebra (result of quantizing the Poisson algebra) acts coincides with the simplest space in which the Lie algebra of commutation relations acts. This coincidence is not necessary for Lie superalgebras.
Received: 08.04.2000 Revised: 02.10.2000
Citation:
D. A. Leites, I. M. Shchepochkina, “How to Quantize the Antibracket”, TMF, 126:3 (2001), 339–369; Theoret. and Math. Phys., 126:3 (2001), 281–306
Linking options:
https://www.mathnet.ru/eng/tmf435https://doi.org/10.4213/tmf435 https://www.mathnet.ru/eng/tmf/v126/i3/p339
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Abstract page: | 687 | Full-text PDF : | 294 | References: | 90 | First page: | 1 |
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