Nearly associative deformation quantization D. V. Vassilevich, F. M. Oliveira
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ArticleSubject(s): деформационное квантование | неассоциативные алгебрыGenre/Form: статьи в журналах Online resources: Click here to access online
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Letters in mathematical physics Vol. 108, № 10. P. 2293-2301Abstract: We study several classes of non-associative algebras as possible candidates for deformation quantization in the direction of a Poisson bracket that does not satisfy Jacobi identities. We show that in fact alternative deformation quantization algebras require the Jacobi identities on the Poisson bracket and, under very general assumptions, are associative. At the same time, flexible deformation quantization algebras exist for any Poisson bracket.
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We study several classes of non-associative algebras as possible candidates for deformation quantization in the direction of a Poisson bracket that does not satisfy Jacobi identities. We show that in fact alternative deformation quantization algebras require the Jacobi identities on the Poisson bracket and, under very general assumptions, are associative. At the same time, flexible deformation quantization algebras exist for any Poisson bracket.
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