Novel symmetries in the modified version of two dimensional Proca theory

Abstract

By exploiting Stueckelberg's approach, we obtain a gauge theory for the two (1+1)-dimensional (2D) Proca theory and demonstrate that this theory is endowed with, in addition to the usual Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetries, the on-shell nilpotent (anti-)co-BRST symmetries, under which the total gauge-fixing term remains invariant. The anticommutator of the BRST and co-BRST (as well as anti-BRST and anti-co-BRST) symmetries define a unique bosonic symmetry in the theory, under which the ghost part of the Lagrangian density remains invariant. To establish connections of the above symmetries with the Hodge theory, we invoke a pseudo-scalar field in the theory. Ultimately, we demonstrate that the full theory provides a field theoretic example for the Hodge theory where the continuous symmetry transformations provide a physical realization of the de Rham cohomological operators and discrete symmetries of the theory lead to the physical realization of the Hodge duality operation of differential geometry. We also mention the physical implications and utility of our present investigation.

arXiv commentLaTeX file, 21 pages, journal reference

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Cited by in corpus (16)

• Modified 2D Proca Theory: Revisited Under BRST and (Anti-)Chiral Superfield Formalisms
• A Massive Field-Theoretic Model for Hodge Theory
• A Free N = 2 Supersymmetric System: Novel Symmetries
• Augmented Superfield Approach to Nilpotent Symmetries in the Modified Version of 2D Proca Theory
• Novel symmetries in an interacting N = 2 supersymmetric quantum mechanical model
• A Quantum Mechanical Example for Hodge Theory
• Massive 4D Abelian 2-Form Theory: Nilpotent Symmetries from the (Anti-)Chiral Superfield Approach
• Modified Proca Theory in Arbitrary and Two Dimensions
• Off-shell nilpotent (anti-)BRST symmetries for a free particle system on a toric geometry: superfield formalism
• A 3D Field-Theoretic Example for Hodge Theory
• Modified St$\ddot{u}$ckelberg Formalism: Free Massive Abelian 2-Form Theory in 4D
• Constraints, Conserved Charges and Extended BRST Algebra for a 3D Field-Theoretic Example for Hodge Theory
• Universal Superspace Unitary Operator for Some Interesting Abelian Models: Superfield Approach
• Superspace Unitary Operator in Superfield Approach to Non-Abelian Gauge Theory with Dirac Fields
• Pseudo-Scalar Field as a Possible Candidate for Phantom Field
• Universal Superspace Unitary Operator and Nilpotent (Anti-)dual BRST Symmetries: Superfield Formalism