Eur. Phys. J. C (2013) 73: 2535
https://doi.org/10.1140/epjc/s10052-013-2535-2

Regular Article - Theoretical Physics

Novel symmetries in the modified version of two dimensional Proca theory

¹ Physics Department, Center of Advanced Studies, Banaras Hindu University, Varanasi, 221 005, U.P., India
² DST Center for Interdisciplinary Mathematical Sciences, Faculty of Science, Banaras Hindu University, Varanasi, 221 005, India

^* e-mail: rpmalik1995@gmail.com

Received: 18 June 2013
Revised: 18 July 2013
Published online: 30 August 2013

Abstract

By exploiting Stueckelberg’s approach, we obtain a gauge theory for the two-dimensional, that is, (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.