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.
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
This publication is cited in the following 7 articles:
Groman P., Leites D., Shchepochkina I., “Defining relations for the exceptional Lie superalgebras of vector fields”, Orbit Method in Geometry and Physics - in Honor of A.A. Kirillov, Progress in Mathematics, 213, 2003, 101–146
D. A. Leites, I. M. Shchepochkina, “How to Quantize the Antibracket”, Theoret. and Math. Phys., 126:3 (2001), 281–306
Grozman, P, “The Shapovalov determinant for the Poisson superalgebras”, Journal of Nonlinear Mathematical Physics, 8:2 (2001), 220
A Frydryszak, “Supersymmetric mechanics with an odd action functional”, J. Phys. A: Math. Gen., 26:23 (1993), 7227
Roberto Floreanini, Dimitry A. Leites, Luc Vinet, “On the defining relations of quantum superalgebras”, Lett Math Phys, 23:2 (1991), 127
Peter Bryant, Lecture Notes in Physics, 311, Complex Differential Geometry and Supermanifolds in Strings and Fields, 1988, 150
D. A. Leites, “Lie superalgebras”, J. Soviet Math., 30:6 (1985), 2481–2512
Citation in format AMSBIB
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