BRST cohomology and Hodge decomposition theorem in Abelian gauge theory

Abstract

We discuss the Becchi-Rouet-Stora-Tyutin (BRST) cohomology and Hodge decomposition theorem for the two dimensional free U(1) gauge theory. In addition to the usual BRST charge, we derive a local, conserved and nilpotent co(dual)-BRST charge under which the gauge-fixing term remains invariant. We express the Hodge decomposition theorem in terms of these charges and the Laplacian operator. We take a single photon state in the quantum Hilbert space and demonstrate the notion of gauge invariance, no-(anti)ghost theorem, transversality of photon and establish the topological nature of this theory by exploiting the concepts of BRST cohomology and Hodge decomposition theorem. In fact, the topological nature of this theory is encoded in the vanishing of the Laplacian operator when equations of motion are exploited. On the two dimensional compact manifold, we derive two sets of topological invariants with respect to the conserved and nilpotent BRST- and co-BRST charges and express the Lagrangian density of the theory as the sum of terms that are BRST- and co-BRST invariants. Mathematically, this theory captures together some of the key features of both Witten- and Schwarz type of topological field theories.

20 pages, LaTeX, no figures, Title and text have been changed, Journal reference is given, some references have been added

References in corpus (1)

• Topological aspects in non-Abelian gauge theory

Cited by in corpus (26)

• Dual BRST symmetry for QED
• A field-theoretic model for Hodge theory
• New local symmetry for QED in two dimensions
• Rigid Rotor as a Toy Model for Hodge Theory
• Abelian p-Form (p = 1, 2, 3) Gauge Theories as the Field Theoretic Models for the Hodge Theory
• Superfield Approach to Symmetries for Matter Fields in Abelian Gauge Theories
• Abelian 2-form gauge theory: special features
• One-Form Abelian Gauge Theory As The Hodge Theory
• Nilpotent Symmetries for QED in Superfield Formalism
• New symmetries for Abelian gauge theory in superfield formulation
• Cohomological aspects of gauge theories: superfield formalism
• On free 4D Abelian 2-form and anomalous 2D Abelian 1-form gauge theories
• Novel symmetries in the modified version of two dimensional Proca theory
• Topological aspects of Abelian gauge theory in superfield formulation
• Superfield approach to a novel symmetry for non-Abelian gauge theory
• Geometrical Aspects Of BRST Cohomology In Augmented Superfield Formalism
• Gauge Transformations, BRST Cohomology and Wigner's Little Group
• Superfield Approach to (Non-)local Symmetries for One-Form Abelian Gauge Theory
• Superfield approach to topological features of non-Abelian gauge theory
• Hodge Duality Operation And Its Physical Applications On Supermanifolds
• Wigner's little group and BRST cohomology for one-form Abelian gauge theory
• Comments on the dual-BRST symmetry
• Twisted N=8, D=2 super Yang-Mills theory as example of a Hodge-type cohomological theory
• Cohomological Operators and Covariant Quantum Superalgebras
• The basic cohomology of the twisted N=16, D=2 super Maxwell theory
• Constraints and Conserved Charges for Modified Massive and Massless Abelian 1-Form and 2-Form Theories: A Brief Review