Physics – Mathematical Physics
Scientific paper
2005-06-14
J.Math.Phys. 46 (2005) 103513
Physics
Mathematical Physics
23 pages
Scientific paper
10.1063/1.2054647
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.
Bashkirov Denis
Giachetta Giovanni
Mangiarotti Luigi
Sardanashvily Gennadi
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