Noether's inverse second theorem in homology terms

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dc.creatorGiachetta, G.
dc.creatorMangiarotti, L.
dc.creatorSardanashvily, G.
dc.date2006-05-23
dc.date.accessioned2026-07-07T07:14:28Z
dc.date.available2026-07-07T07:14:28Z
dc.descriptionA 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.
dc.description27 pages
dc.identifierhttps://arxiv.org/abs/math/0605618
dc.identifierhttp://arxiv.org/abs/math/0605618
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112890
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subject58A20; 58C50; 58J70; 70S05
dc.titleNoether's inverse second theorem in homology terms
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