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.
REFERENCES
1.
D.
Bashkirov
, G.
Giachetta
, L.
Mangiarotti
, and G.
Sardanashvily
, J. Phys. A
38
, 5239
(2005
).2.
D.
Bashkirov
, G.
Giachetta
, L.
Mangiarotti
, and G.
Sardanashvily
, J. Math. Phys.
46
, 053517
(2005
).3.
I.
Batalin
and G.
Vilkovisky
, Nucl. Phys. B
234
, 106
(1984
).4.
J.
Gomis
, J.
París
, and S.
Samuel
, Phys. Rep.
295
, 1
(1995
).5.
J.
Fisch
, M.
Henneaux
, J.
Stasheff
, and C.
Teitelboim
, Commun. Math. Phys.
120
, 379
(1989
).6.
J.
Fisch
and M.
Henneaux
, Commun. Math. Phys.
128
, 627
(1990
).7.
G.
Barnich
, F.
Brandt
, and M.
Henneaux
, Phys. Rep.
338
, 439
(2000
).8.
9.
G.
Giachetta
, L.
Mangiarotti
, and G.
Sardanashvily
, Commun. Math. Phys.
259
, 103
(2005
).10.
C.
Bartocci
, U.
Bruzzo
, and D.
Hernández Ruipérez
, The Geometry of Supermanifolds
(Kluwer
, Dordrecht, 1991
).11.
G.
Giachetta
, L.
Mangiarotti
, and G.
Sardanashvily
, Geometric and Algebraic Topological Methods in Quantum Mechanics
(World Scientific
, Singapore, 2005
).12.
A.
Rennie
, K-Theory
28
, 127
(2003
).13.
D.
Fuks
, Cohomology of Infinite-Dimensional Lie Algebras
(Consultants Bureau
, New York, 1986
).14.
15.
F.
Brandt
, Lett. Math. Phys.
55
, 149
(2001
).© 2005 American Institute of Physics.
2005
American Institute of Physics
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