One-Form Abelian Gauge Theory As The Hodge Theory

Abstract

We demonstrate that the two (1 + 1)-dimensional (2D) free 1-form Abelian gauge theory provides an interesting field theoretical model for the Hodge theory. The physical symmetries of the theory correspond to all the basic mathematical ingredients that are required in the definition of the de Rham cohomological operators of differential geometry. The conserved charges, corresponding to the above continuous symmetry transformations, constitute an algebra that is reminiscent of the algebra obeyed by the de Rham cohomological operators. The topological features of the above theory are discussed in terms of the BRST and co-BRST operators. The super de Rham cohomological operators are exploited in the derivation of the nilpotent (anti-)BRST, (anti-)co-BRST symmetry transformations and the equations of motion for all the fields of the theory, within the framework of the superfield formulation. The derivation of the equations of motion, by exploiting the super Laplacian operator, is a completely new result in the framework of the superfield approach to BRST formalism. In an Appendix, the interacting 2D Abelian gauge theory (where there is a coupling between the U(1) gauge field and the Dirac fields) is also shown to provide a tractable field theoretical model for the Hodge theory.

arXiv commentLaTeX file, 39 pages, brief review, journal version

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Cited by in corpus (25)

• A field-theoretic model for Hodge theory
• Abelian p-Form (p = 1, 2, 3) Gauge Theories as the Field Theoretic Models for the Hodge Theory
• Modified 2D Proca Theory: Revisited Under BRST and (Anti-)Chiral Superfield Formalisms
• A Massive Field-Theoretic Model for Hodge Theory
• Novel symmetries in the modified version of two dimensional Proca theory
• Novel discrete symmetries in the general N = 2 supersymmetric quantum mechanical model
• Dual-BRST symmetry: 6D Abelian 3-form gauge theory
• Self-Dual Chiral Boson: Augmented Superfield Approach
• Novel symmetries in N = 2 supersymmetric quantum mechanical models
• A Free N = 2 Supersymmetric System: Novel Symmetries
• Free Abelian 2-Form Gauge Theory: BRST Approach
• Augmented Superfield Approach to Nilpotent Symmetries in the Modified Version of 2D Proca Theory
• Novel Symmetries in Christ-Lee Model
• Absolute anticommutativity of the nilpotent symmetries in the Hamiltonian formalism: free Abelian 2-form gauge theory
• Canonical brackets of a toy model for the Hodge theory without its canonical conjugate momenta
• Off-shell nilpotent (anti-)BRST symmetries for a free particle system on a toric geometry: superfield formalism
• Novel symmetries in Weyl-invariant gravity with massive gauge field
• N = 2 Supersymmetric Harmonic Oscillator: Basic Brackets Without Canonical Conjugate Momenta
• Basic Brackets of a 2D Model for the Hodge Theory without its Canonical Conjugate Momenta
• Universal Superspace Unitary Operator for Some Interesting Abelian Models: Superfield Approach
• Some Novel Features in 2D Non-Abelian Theory: BRST Approach
• Supervariable approach to particle on a torus knot: A model for Hodge theory
• Christ-Lee Model: Augmented Supervariable Approach
• Revisiting Novel Symmetries in Coupled $\mathcal{N}=2$ Supersymmetric Quantum Systems: Examples and Supervariable Approach
• Nilpotent (Anti-)BRST and (Anti-)co-BRST Symmetries in 2D non-Abelian Gauge Theory: Some Novel Observations