Isomorphisms between the Batalin-Vilkovisky antibracket and the Poisson bracket

Abstract

One may introduce at least three different Lie algebras in any Lagrangian field theory : (i) the Lie algebra of local BRST cohomology classes equipped with the odd Batalin-Vilkovisky antibracket, which has attracted considerable interest recently~; (ii) the Lie algebra of local conserved currents equipped with the Dickey bracket~; and (iii) the Lie algebra of conserved, integrated charges equipped with the Poisson bracket. 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 freedom, (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 detailed analysis of the local BRST cohomology classes in the Hamiltonian formalism allows one to prove an isomorphism theorem between the antibracket and the extended Poisson bracket of Batalin, Fradkin and Vilkovisky.

36 pages Latex file

Cited by in corpus (31)

• Covariant theory of asymptotic symmetries, conservation laws and central charges
• Surface charge algebra in gauge theories and thermodynamic integrability
• Comments on holographic current algebras and asymptotically flat four dimensional spacetimes at null infinity
• Superfield BRST Charge and the Master Action
• Parent form for higher spin fields on anti-de Sitter space
• A Poincare lemma for sigma models of AKSZ type
• An Introduction to the Covariant Quantization of Superstrings
• Hamiltonian BRST and Batalin-Vilkovisky formalisms for second quantization of gauge theories
• Rigid Symmetries and Conservation Laws in Non-Lagrangian Field Theory
• Lie n-algebras of BPS charges
• BRST analysis of general mechanical systems
• Freedman-Townsend vertex from Hamiltonian BRST cohomology
• Hamiltonian BRST deformation of a class of n-dimensional BF-type theories
• Hamiltonian cohomological derivation of four-dimensional nonlinear gauge theories
• Covariant canonical formulations of classical field theories
• Local BRST cohomology in (non-)Lagrangian field theory
• Extended BRST cohomology, consistent deformations and anomalies of four-dimensional supersymmetric gauge theories
• Deformations of vector-scalar models
• Variational Tricomplex, Global Symmetries and Conservation Laws of Gauge Systems
• Gauge Symmetries of the Master Action
• Variational tricomplex of a local gauge system, Lagrange structure and weak Poisson bracket
• PT-symmetry breaking hamiltonian interactions in BF models
• Lagrange Anchor and Characteristic Symmetries of Free Massless Fields
• BRST Formalism and Zero Locus Reduction
• Canonical Transformations of Local Functionals and sh-Lie Structures
• Geometrical representation of Euclidean general relativity in the canonical formalism
• Lie and Leibniz Algebras of Lower-Degree Conservation Laws
• Homological evolutionary vector fields in Korteweg-de Vries, Liouville, Maxwell, and several other models
• A first look at Weyl anomalies in shape dynamics
• Superfield algorithm for higher order gauge field theories
• Functionals and the Quantum Master Equation