Higher‐Stage Noether Identities and Second Noether Theorems

G. Sardanashvily

Advances in Mathematical Physics, 2015, vol. 2015, issue 1

Abstract: The direct and inverse second Noether theorems are formulated in a general case of reducible degenerate Grassmann‐graded Lagrangian theory of even and odd variables on graded bundles. Such Lagrangian theory is characterized by a hierarchy of nontrivial higher‐stage Noether identities which is described in the homology terms. If a certain homology regularity condition holds, one can associate with a reducible degenerate Lagrangian the exact Koszul–Tate chain complex possessing the boundary operator whose nilpotentness is equivalent to all complete nontrivial Noether and higher‐stage Noether identities. The second Noether theorems associate with the above‐mentioned Koszul–Tate complex a certain cochain sequence whose ascent operator consists of the gauge and higher‐order gauge symmetries of a Lagrangian system. If gauge symmetries are algebraically closed, this operator is extended to the nilpotent BRST operator which brings the above‐mentioned cochain sequence into the BRST complex and provides a BRST extension of an original Lagrangian.

Date: 2015
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https://doi.org/10.1155/2015/127481

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:127481

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