The antifield Koszul-Tate complex of reducible Noether identities
arXiv:math-ph/0506034 · doi:10.1063/1.2054647
Abstract
A generic degenerate Lagrangian system of even and odd fields is examined in algebraic terms of the Grassmann-graded variational bicomplex. Its Euler-Lagrange operator obeys Noether identities which need not be independent, but satisfy first-stage Noether identities, and so on. We show that, if a certain necessary and sufficient condition holds, one can associate to a degenerate Lagrangian system the exact Koszul-Tate complex with the boundary operator whose nilpotency condition restarts all its Noether and higher-stage Noether identities. This complex provides a sufficient analysis of the degeneracy of a Lagrangian system for the purpose of its BV quantization.
23 pages
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- On necessary and sufficient conditions of the BV quantization of a generic Lagrangian field system
- Remark on the Serre-Swan theorem for graded manifolds
- On incompleteness of classical field theory
- Noether's inverse second theorem in homology terms
- Axiomatic quantum field theory. Jet formalism
- Grassmann-graded Lagrangian theory of even and odd variables