Eur. Phys. J. C (2010) 68: 325-335
https://doi.org/10.1140/epjc/s10052-010-1313-7

Regular Article - Theoretical Physics

Rigid rotor as a toy model for Hodge theory

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

^* e-mail: malik@bhu.ac.in

Received: 20 February 2010
Published online: 27 April 2010

Abstract

We apply the superfield approach to the toy model of a rigid rotor and show the existence of the nilpotent and absolutely anticommuting Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry transformations, under which, the kinetic term and the action remain invariant. Furthermore, we also derive the off-shell nilpotent and absolutely anticommuting (anti-) co-BRST symmetry transformations, under which, the gauge-fixing term and the Lagrangian remain invariant. The anticommutator of the above nilpotent symmetry transformations leads to the derivation of a bosonic symmetry transformation, under which, the ghost terms and the action remain invariant. Together, the above transformations (and their corresponding generators) respect an algebra that turns out to be a physical realization of the algebra obeyed by the de Rham cohomological operators of differential geometry. Thus, our present model is a toy model for the Hodge theory.