My new
article: G.Sardanashvily, Higher-stage Noether identities and second Noether
theorems, Advances in Mathematical
Physics, v 2015 (2015) 127481(#)
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 non-trivial higher-stage Noether identities which is described in
the homology terms. If a certain homology regularity conditions holds, one can associate
to a reducible degenerate Lagrangian the exact Koszul – Tate chain complex
possessing the boundary operator whose nilpotentness is equivalent to all
complete non-trivial Noether and higher-stage Noether identities. The second
Noether theorems associate
to 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.
