General Form of the *-Commutator on the Grassmann Algebra
Tóm tắt
The general form of the *-commutator on the Grassmann algebra treated as a deformation of the conventional Poisson bracket is investigated. It is shown that in addition to the Moyal *-commutator, there exist other deformations of the Poisson bracket on the Grassman algebra (one additional deformation for even and odd n, where n is the number of the Grassmann algebra generators) that are not reducible to the Moyal *-commutator by a similarity transformation.
Tài liệu tham khảo
F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowich, and D. Sternheimer, Ann. Phys., 111, 61 (1978).
F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowich, and D. Sternheimer, Ann. Phys., 111, 111 (1978).
M. V. Karasev and V. P. Maslov, Nonlinear Poisson Brackets: Geometry and Quantization [in Russian], Nauka, Moscow (1991); English transl., Am. Math. Soc., Providence (1993).
B. Fedosov, Deformation Quantization and Index Theory, Akademie, Berlin (1996).
M. Kontsevich, “Deformation quantization of Poisson manifolds: I,” q-alg/9709040 (1997).
J. E. Moyal, Proc. Cambridge Philos. Soc., 45, 99 (1949).