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Degenerate odd poisson bracket on grassmann variables

  • Elementary Particles and Fields
  • Theory
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Abstract

A linear degenerate odd Poisson bracket (antibracket) realized solely on Grassmann variables is proposed. It is revealed that this bracket has at once three Grassmann-odd nilpotent Δ-like differential operators of the first, second and third orders with respect to the Grassmann derivatives. It is shown that these Δ-like operators, together with the Grassmann-odd nilpotent Casimir function of this bracket, form a finite-dimensional Lie superalgebra.

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Authors and Affiliations

  1. National Research Center, Kharkov Institute for Physics and Technology, Akademicheskaya ul. 1, Kharkov, 310108, Ukraine

    V. A. Soroka

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  1. V. A. Soroka
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Additional information

From Yadernaya Fizika, Vol. 63, No. 5, 2000, pp. 988–990.

Original English Text Copyright © 2000 by Soroka.

This article was submitted by the author in English.

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Soroka, V.A. Degenerate odd poisson bracket on grassmann variables. Phys. Atom. Nuclei 63, 915–917 (2000). https://doi.org/10.1134/1.855725

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  • DOI: https://doi.org/10.1134/1.855725

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