Abstract
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.
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Tyutin, I.V. General Form of the *-Commutator on the Grassmann Algebra. Theoretical and Mathematical Physics 128, 1271–1292 (2001). https://doi.org/10.1023/A:1012320121612
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DOI: https://doi.org/10.1023/A:1012320121612