The Batalin-Vilkovisky cohomology of the spinning particle

Open Access
Regular Article - Theoretical Physics


We show that the axiom of Felder and Kazhdan [4] on the vanishing of the cohomology groups in negative degree associated to solutions of the classical master equation in the Batalin-Vilkovisky formalism is violated by the spinning particle in a flat background coupled to D = 1 supergravity. In this model, there are nontrivial cohomology groups in all negative degrees, regardless of the dimension of the spacetime in which the spinning particle is propagating.


BRST Quantization Supergravity Models Differential and Algebraic Geometry 


Open Access

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  1. [1]
    G. Barnich, F. Brandt and M. Henneaux, Local BRST cohomology in gauge theories, Phys. Rept. 338 (2000) 439 [hep-th/0002245] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    L. Brink, S. Deser, B. Zumino, P. Di Vecchia and P.S. Howe, Local Supersymmetry for Spinning Particles, Phys. Lett. B 64 (1976) 435 [Erratum ibid. B 68 (1977) 488] [INSPIRE].
  3. [3]
    K. Costello, Renormalization and effective field theory, American Mathematical Society, Providence RI U.S.A. (2011) [ISBN: 978-0-8218-5288-0, 978-1-4704-1397-2] [Math. Surveys Monogr. 170 (2011) 1].Google Scholar
  4. [4]
    G. Felder, D. Kazhdan and T.M. Schlank, The classical master equation, in Perspectives in representation theory, American Mathematical Society, Providence RI U.S.A. (2014), Contemp. Math. 610 (2014) 79 [arXiv:1212.1631] [INSPIRE].

Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Department of MathematicsNorthwestern UniversityEvanstonU.S.A.

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