A field-theoretic model for Hodge theory
arXiv:0807.2306 · doi:10.1140/epjc/s10052-008-0758-4
Abstract
We demonstrate that the four (3 + 1)-dimensional free Abelian 2-form gauge theory presents a tractable field theoretical model for the Hodge theory where the well-defined symmetry transformations correspond to the de Rham cohomological operators of differential geometry. The conserved charges, corresponding to the above continuous symmetry transformations, obey an algebra that is reminiscent of the algebra obeyed by the cohomological operators. The discrete symmetry transformation of the theory represents the realization of the Hodge duality operation that exists in the relationship between the exterior and co-exterior derivatives of differential geometry. Thus, we provide the realizations of all the mathematical quantities, associated with the de Rham cohomological operators, in the language of the symmetries of the present 4D free Abelian 2-form gauge theory.
LaTeX file, 24 pages, journal reference is given
References in corpus (19)
- Phase transitions in BaTiO from first principles
- Duality, Self-Duality, Sources and Charge Quantization in Abelian N-Form Theories
- A New Symmetry for QED
- New topological field theories in two dimensions
- Hodge decomposition theorem for Abelian two form gauge theory
- BRST, anti-BRST and gerbes
- New local symmetry for QED in two dimensions
- Cohomological aspects of Abelian gauge theory
- BRST cohomology and Hodge decomposition theorem in Abelian gauge theory
- Abelian 2-form gauge theory: special features
- One-Form Abelian Gauge Theory As The Hodge Theory
- Comment on ``A New Symmetry for QED'' and ``Relativistically Covariant Symmetry in QED''
- Time evolution in general gauge theories defined on inner product spaces
- The Several Guises of the BRST Symmetry
- Gauge Transformations, BRST Cohomology and Wigner's Little Group
- Free Abelian 2-Form Gauge Theory: BRST Approach
- Reply to Comment hep-th/9509028
- Vector-Tensor Duality
- (Anti-)dual-BRST symmetries: Abelian 2-form gauge theory
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- 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
- Supersymmetric Oscillator: Novel Symmetries
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- A Free N = 2 Supersymmetric System: Novel Symmetries
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- Noether Theorem and Nilpotency Property of the (Anti-)BRST Charges in the BRST Formalism: A Brief Review
- Augmented Superfield Approach to Nilpotent Symmetries in the Modified Version of 2D Proca Theory
- Augmented Superfield Approach to Gauge-invariant Massive 2-Form Theory
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- Modified Proca Theory in Arbitrary and Two Dimensions
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- Off-shell nilpotent (anti-)BRST symmetries for a free particle system on a toric geometry: superfield formalism
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- Nilpotent and absolutely anticommuting symmetries in the Freedman-Townsend model: augmented superfield formalism
- Absolute anticommutativity of the nilpotent symmetries in the Hamiltonian formalism: free Abelian 2-form gauge theory
- N = 2 Supersymmetric Harmonic Oscillator: Basic Brackets Without Canonical Conjugate Momenta
- A 3D Field-Theoretic Example for Hodge Theory
- Notoph Gauge Theory: Superfield Formalism
- On augmented superfield approach to vector Schwinger model
- Nilpotent Symmetries and Curci-Ferrari Type Restrictions in 2D Non-Abelian Gauge Theory: Superfield Approach
- Basic Brackets of a 2D Model for the Hodge Theory without its Canonical Conjugate Momenta
- 3D Jackiw-Pi Model: (Anti-)Chiral Superfield Approach to BRST Formalism
- Various forms of BRST symmetry in Abelian 2-form gauge theory
- A Field-Theoretic Model: Discrete Duality Symmetry
- Nilpotency Property, Physicality Criteria, Constraints and Standard BRST Algebra: A 4D Field-Theoretic System
- (3+1)-Dimensional Topologically Massive 2-form Gauge Theory: Geometrical Superfield Approach
- Revisiting Novel Symmetries in Coupled Supersymmetric Quantum Systems: Examples and Supervariable Approach
- Supervariable approach to particle on a torus knot: A model for Hodge theory
- Continuous and Discrete Symmetries in a 4D Field-Theoretic Model: Symmetry Operators and Their Algebraic Structures
- A note on the (anti-)BRST invariant Lagrangian densities for the free abelian 2-form gauge theory
- Constraints and Conserved Charges for Modified Massive and Massless Abelian 1-Form and 2-Form Theories: A Brief Review
- Nilpotent (Anti-)BRST and (Anti-)co-BRST Symmetries in 2D non-Abelian Gauge Theory: Some Novel Observations