English

The Batalin-Vilkovisky formalism of the spinning particle

Mathematical Physics 2018-01-16 v3 High Energy Physics - Theory math.MP

Abstract

We show that the axiom of Felder and Kazhdan 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.

Keywords

Cite

@article{arxiv.1511.02135,
  title  = {The Batalin-Vilkovisky formalism of the spinning particle},
  author = {Ezra Getzler},
  journal= {arXiv preprint arXiv:1511.02135},
  year   = {2018}
}

Comments

17 pages In v2, we correct an error in the calculation of cohomology in degree -1, extend our calculation to positive degrees, and construct the transgression classes by a uniform method. In v3, we calculate the Lie bracket on the BV cohomology, and make a number of further corrections, especially to the definition of the filtration used in the spectral sequence used to prove the main theorem