On the uniqueness of the Moyal structure of phase-space functions

Details On the uniqueness of the Moyal structure of phase-space functions On the uniqueness of the Moyal structure of phase-space functions

1996-05-13

arxiv.org/abs/q-alg/9605018v1

Mathematics

Quantum Algebra

13 pages, Latex

Scientific paper

10.1088/0305-4470/30/13/033

It is shown that the only associative algebras with a trivial center defined on functions of $\Rl^N$ by an integral kernel are generalized Moyal algebras, corresponding to some particular operator ordering. Similarly, the only such Lie algebras are generalized Moyal or Poisson Lie algebras. In both cases these structures are isomorphic respectively to the Moyal algebra, the Moyal Lie algebra and the Poisson Lie algebra. These results are independent of $N$, which is necessarily even, and generalize previous work on the subject.

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