• Open Access

BFV extensions for mechanical systems with Lie-2 symmetry

Aliaksandr Hancharuk and Thomas Strobl
Phys. Rev. D 107, 025014 – Published 24 January 2023

Abstract

We consider mechanical systems on T*M with possibly irregular and reducible first class constraints linear in the momenta, which thus correspond to singular foliations on M. According to a recent result, the latter ones have a Lie-infinity algebroid (M,Q) covering them, where we restrict to the case of Lie-2 algebroids. We propose to consider T*M as a potential Batalin-Fradkin-Vilkovisky (BFV) extended phase space of the constrained system, such that the canonical lift of the nilpotent vector field Q yields automatically a solution to the BFV master equation. We show that in this case, the BFV extension of the Hamiltonian, providing a second corner stone of the BFV formalism, may be obstructed. We identify the corresponding complex governing this second extension problem explicitly (the first extension problem was circumvented by means of the lift of the Lie-2 algebroid structure). We repeatedly come back to the example of angular momenta on T*R3: in this procedure, the standard free Hamiltonian does not have a BFV extension—while it does so on T*(R3\{0}), with a relatively involved ghost contribution singular at the origin.

  • Received 2 May 2022
  • Accepted 3 January 2023

DOI:https://doi.org/10.1103/PhysRevD.107.025014

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

Aliaksandr Hancharuk and Thomas Strobl

  • Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France

Article Text

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Issue

Vol. 107, Iss. 2 — 15 January 2023

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