The sh Lie structure of Poisson brackets in field theory

Details The sh Lie structure of Poisson brackets in field theory The sh Lie structure of Poisson brackets in field theory

1997-02-25

arxiv.org/abs/hep-th/9702176v1

Physics

High Energy Physics

High Energy Physics - Theory

24 pages Latex file

Scientific paper

10.1007/s002200050278

A general construction of an sh Lie algebra from a homological resolution of a Lie algebra is given. It is applied to the space of local functionals equipped with a Poisson bracket, induced by a bracket for local functions along the lines suggested by Gel'fand, Dickey and Dorfman. In this way, higher order maps are constructed which combine to form an sh Lie algebra on the graded differential algebra of horizontal forms. The same construction applies for graded brackets in field theory such as the Batalin-Fradkin-Vilkovisky bracket of the Hamiltonian BRST theory or the Batalin-Vilkovisky antibracket.

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