Noether's inverse second theorem in homology terms

G. Giachetta; L. Mangiarotti; G. Sardanashvily

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Noether's inverse second theorem in homology terms

G. Giachetta·L. Mangiarotti·G. Sardanashvily

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Abstract

A generic degenerate Lagrangian system of even and odd variables on an arbitrary smooth manifold is examined in 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. However, non-trivial higher-stage Noether identities are ill defined, unless a certain homology condition holds. We show that, under this condition, there exists the exact Koszul-Tate chain complex whose boundary operator produces all non-trivial Noether and higher-stage Noether identities of an original Lagrangian system. Noether's inverse second theorem that we prove associates to this complex a cochain sequence whose ascent operator provides all gauge and higher-stage gauge supersymmetries of an original Lagrangian.

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BibTeX RIS

G. Giachetta, L. Mangiarotti, G. Sardanashvily. 2006-05-23. Noether's inverse second theorem in homology terms. https://arxiv.org/abs/math/0605618

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