Hodge decomposition theorem for Abelian two form gauge theory
arXiv:hep-th/0004145 · doi:10.1088/0305-4470/33/40/312
Abstract
We show that the BRST/anti-BRST invariant 3+1 dimensional 2-form gauge theory has further nilpotent symmetries (dual BRST /anti-dual BRST) that leave the gauge fixing term invariant. The generator for the dual BRST symmetry is analogous to the co-exterior derivative of differential geometry. There exists a bosonic symmetry which keeps the ghost terms invariant and it turns out to be the analogue of the Laplacian operator. The Hodge duality operation is shown to correspond to a discrete symmetry in the theory. The generators of all these continuous symmetries are shown to obey the algebra of the de Rham cohomology operators of differential geometry. We derive the extended BRST algebra constituted by six conserved charges and discuss the Hodge decomposition theorem in the quantum Hilbert space of states.
LaTeX, 18 pages, no figures, minor corrections, references updated, typos corrected, journal reference given
References in corpus (18)
- Information-theoretic characterization of quantum chaos
- A New Symmetry for QED
- Bosonisation and Duality Symmetry in the Soldering Formalism
- Constrained Dynamics of the Coupled Abelian Two-Form
- Cohomological aspects of Abelian gauge theory
- Topological aspects in non-Abelian gauge theory
- Gauge fixing and coBRST
- Comment on ``A New Symmetry for QED'' and ``Relativistically Covariant Symmetry in QED''
- Reducible systems and embedding procedures in the canonical formalism
- Time evolution in general gauge theories defined on inner product spaces
- Duality and Massive Gauge Invariant Theories
- Relativistically Covariant Symmetry in QED
- Lie algebra cohomology and group structure of gauge theories
- Higher order BRST and anti-BRST operators and cohomology for compact Lie algebras
- Topologically Massive Abelian Gauge Theory From BFT Hamiltonian Embedding of A First-order Theory
- Reply to Comment hep-th/9509028
- Vector-Tensor Duality
- On the constrained structure of duality symmetric Maxwell theory
Cited by in corpus (39)
- New topological field theories in two dimensions
- A field-theoretic model for Hodge theory
- Abelian 2-form gauge theory: superfield formalism
- BRST, anti-BRST and gerbes
- 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 A Spinning Relativistic Particle In Augmented Superfield Formalism
- Nilpotent Symmetries for QED in Superfield Formalism
- New symmetries for Abelian gauge theory in superfield formulation
- Cohomological aspects of gauge theories: superfield formalism
- Novel symmetries in the modified version of two dimensional Proca theory
- The model for self-dual chiral bosons as a Hodge theory
- Superfield approach to BRST cohomology
- 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
- Nilpotent Symmetries of a 4D Model of the Hodge Theory: Augmented (Anti-)Chiral Superfield Formalism
- Absolutely anticommuting (anti-)BRST symmetry transformations for topologically massive Abelian gauge theory
- Superfield approach to topological features of non-Abelian gauge theory
- Superfield Approach to (Non-)local Symmetries for One-Form Abelian Gauge Theory
- Free Abelian 2-Form Gauge Theory: BRST Approach
- Hodge Duality Operation And Its Physical Applications On Supermanifolds
- Augmented Superfield Approach to Gauge-invariant Massive 2-Form Theory
- Comments on the dual-BRST symmetry
- Nilpotent symmetry invariance in the superfield formulation: the (non-)Abelian 1-form gauge theories
- Absolute anticommutativity of the nilpotent symmetries in the Hamiltonian formalism: free Abelian 2-form gauge theory
- Notoph Gauge Theory: Superfield Formalism
- The Poincare lemma for codifferential, anticoexact forms, and applications to physics
- Constraints, Conserved Charges and Extended BRST Algebra for a 3D Field-Theoretic Example for Hodge Theory
- Pseudo-Scalar Field as a Possible Candidate for Phantom Field
- Cohomological Operators and Covariant Quantum Superalgebras
- Nilpotency Property, Physicality Criteria, Constraints and Standard BRST Algebra: A 4D Field-Theoretic System
- Various forms of BRST symmetry in Abelian 2-form gauge theory
- Constraints and Conserved Charges for Modified Massive and Massless Abelian 1-Form and 2-Form Theories: A Brief Review
- A note on the (anti-)BRST invariant Lagrangian densities for the free abelian 2-form gauge theory