Lie algebra cohomology and group structure of gauge theories

Abstract

We explicitly construct the adjoint operator of coboundary operator and obtain the Hodge decomposition theorem and the Poincaré duality for the Lie algebra cohomology of the infinite-dimensional gauge transformation group. We show that the adjoint of the coboundary operator can be identified with the BRST adjoint generator $Q^{†}$ for the Lie algebra cohomology induced by BRST generator $Q$. We also point out an interesting duality relation - Poincaré duality - with respect to gauge anomalies and Wess-Zumino-Witten topological terms. We consider the consistent embedding of the BRST adjoint generator $Q^{†}$ into the relativistic phase space and identify the noncovariant symmetry recently discovered in QED with the BRST adjoint Nöther charge $Q^{†}$.

24 pages, RevTex, Revised version submitted to J. Math. Phys

References in corpus (7)

• General Solution of the Consistency Equation
• General Effective Actions
• A New Symmetry for QED
• Algebraic characterization of the Wess-Zumino consistency conditions in gauge theories
• Invariant Effective Actions, Cohomology of Homogeneous Spaces and Anomalies
• Comment on ``A New Symmetry for QED'' and ``Relativistically Covariant Symmetry in QED''
• Reply to Comment hep-th/9509028

Cited by in corpus (14)

• Dual BRST symmetry for QED
• New topological field theories in two dimensions
• Hodge decomposition theorem for Abelian two form gauge theory
• New local symmetry for QED in two dimensions
• Cohomological aspects of Abelian gauge theory
• BRST cohomology and Hodge decomposition theorem in Abelian gauge theory
• One-Form Abelian Gauge Theory As The Hodge Theory
• Cohomological aspects of gauge theories: superfield formalism
• Higher order BRST and anti-BRST operators and cohomology for compact Lie algebras
• Finite Nilpotent BRST transformations in Hamiltonian formulation
• New forms of BRST symmetry in rigid rotor
• Novel Symmetries in Vector Schwinger Model
• Note on the dual BRST Symmetry in U(1) Gauge Theory
• Various forms of BRST symmetry in Abelian 2-form gauge theory