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The sh Lie Structure of Poisson Brackets in Field Theory

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Abstract:

A general construction of an sh Lie algebra (L ∞-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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Authors and Affiliations

  1. Center for Gravitational Physics and Geometry, The Pennsylvania State University, 104 Davey Laboratory, University Park, PA 16802, USA, , , , , , US

    G. Barnich

  2. Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA, , , , , , US

    R. Fulp & T. Lada

  3. Department of Mathematics, The University of North Carolina at Chapel Hill, Phillips Hall, Chapel Hill, NC 27599-3250, USA, , , , , , US

    J. Stasheff

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  1. G. Barnich
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  2. R. Fulp
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  3. T. Lada
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  4. J. Stasheff
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Received: 5 March 1997 / Accepted: 21 May 1997

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Barnich, G., Fulp, R., Lada, T. et al. The sh Lie Structure of Poisson Brackets in Field Theory . Comm Math Phys 191, 585–601 (1998). https://doi.org/10.1007/s002200050278

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  • DOI: https://doi.org/10.1007/s002200050278

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