ISOMORPHISMS BETWEEN THE BATALIN-VILKOVISKY ANTIBRACKET AND THE POISSON BRACKET

One may introduce at least three different Lie algebras in any Lagrang ian held theory: (i) the Lie algebra of local BRST cohomology classes equipped with the odd Batalin-Vilkovisky antibracket, which has attrac ted considerable interest recently; (ii) the Lie algebra of local cons erved currents equipped with the Dickey bracket; and (iii) the Lie alg ebra of conserved, integrated charges equipped with the Poisson bracke t. We show in this paper that the subalgebra of (i) in ghost number -1 and the other two algebras are isomorphic for a field theory without gauge invariance. We also prove that, in the presence of a gauge freed om, (ii) is still isomorphic to the subalgebra of (i) in ghost number -1, while (iii) is isomorphic to the quotient of (ii) by the ideal of currents without charge. In ghost number different from -1, a more det ailed analysis of the local BRST cohomology classes in the Hamiltonian formalism allows one to prove an isomorphism theorem between the anti bracket and the extended Poisson bracket of Batalin, Fradkin, and Vilk ovisky. (C) 1996 American Institute of Physics.