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Advances in High Energy Physics
Volume 2017, Article ID 6124189, 11 pages
Research Article

Double Hodge Theory for a Particle on Torus

Department of Physics, Banaras Hindu University, Varanasi 221005, India

Correspondence should be addressed to Vipul Kumar Pandey; moc.liamg@isanaravlupiv

Received 1 July 2017; Accepted 31 October 2017; Published 27 November 2017

Academic Editor: Edward Sarkisyan-Grinbaum

Copyright © 2017 Vipul Kumar Pandey and Bhabani Prasad Mandal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


We investigate all possible nilpotent symmetries for a particle on torus. We explicitly construct four independent nilpotent BRST symmetries for such systems and derive the algebra between the generators of such symmetries. We show that such a system has rich mathematical properties and behaves as double Hodge theory. We further construct the finite field dependent BRST transformation for such systems by integrating the infinitesimal BRST transformation systematically. Such a finite transformation is useful in realizing the various theories with toric geometry.