Modified Proca Theory in Arbitrary and Two Dimensions

Abstract

We demonstrate that the standard Stueckelberg-modified Proca theory (i.e. a massive Abelian 1-form theory) respects the classical gauge and corresponding quantum (anti-)BRST symmetry transformations in any arbitrary dimension of spacetime within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. We further show that the Stueckelberg formalism gets modified in the two (1+1)-dimensions of spacetime due to a couple of discrete duality symmetries in the theory which turn out to be responsible for the existence of the nilpotent (anti-)co-BRST symmetry transformations corresponding to the nilpotent (anti-)BRST symmetry transformations of our theory. These nilpotent symmetries exist together in the modified version of the two (1+1)-dimensional (2D) Proca theory. We provide the mathematical basis for the modification of the Stueckelberg-technique, the existence of the discrete duality as well as the continuous (anti-)co-BRST symmetry transformations in the 2D modified version of Proca theory.

LaTeX file, 13 pages, minor changes in the text, journal reference given

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• Pseudo-Scalar Field as a Possible Candidate for Phantom Field
• Constraints and Conserved Charges for Modified Massive and Massless Abelian 1-Form and 2-Form Theories: A Brief Review