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Rigid rotor as a toy model for Hodge theory

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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.

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Authors and Affiliations

  1. Physics Department, Centre of Advanced Studies, Banaras Hindu University, Varanasi, 221 005, U.P., India

    Saurabh Gupta & R. P. Malik

  2. DST Centre for Interdisciplinary Mathematical Sciences, Faculty of Science, Banaras Hindu University, Varanasi, 221 005, India

    R. P. Malik

Authors
  1. Saurabh Gupta
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  2. R. P. Malik
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Correspondence to R. P. Malik.

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Gupta, S., Malik, R.P. Rigid rotor as a toy model for Hodge theory. Eur. Phys. J. C 68, 325–335 (2010). https://doi.org/10.1140/epjc/s10052-010-1313-7

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  • DOI: https://doi.org/10.1140/epjc/s10052-010-1313-7

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