Dualities between Poisson brackets and antibrackets

Abstract

Recently it has been shown that antibrackets may be expressed in terms of Poisson brackets and vice versa for commuting functions in the original bracket. Here we also introduce generalized brackets involving higher antibrackets or higher Poisson brackets where the latter are of a new type. We give generating functions for these brackets for functions in arbitrary involutions in the original bracket. We also give master equations for generalized Maurer-Cartan equations. The presentation is completely symmetric with respect to Poisson brackets and antibrackets.

24 pages,Latexfile,corrected (2.7-8) and removed text between (2.9) and (2.10)

References in corpus (6)

• Quantum antibrackets
• Non-Abelian Antibrackets
• Open groups of constraints - Integrating arbitrary involutions
• Batalin-Vilkovisky Formalism and Integration Theory on Manifolds
• Quantum Sp(2)-antibrackets and open groups
• Antisymplectic Gauge Theories

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• Closed description of arbitrariness in resolving quantum master equation
• BRST Formalism and Zero Locus Reduction
• Gauge Independence in a Higher-Order Lagrangian Formalism via Change of Variables in the Path Integral
• The BV formalism for L${}_{\infty }$-algebras
• Superfield Hamiltonian quantization in terms of quantum antibrackets
• Path Integral Formulation with Deformed Antibracket
• Reducible Gauge Algebra of BRST-Invariant Constraints
• Does the nontrivially deformed field-antifield formalism exist?