FLPR model: Nilpotent (anti-)co-BRST symmetries

Abstract

We demonstrate the existence of a set of novel off-shell nilpotent and absolutely anticommuting continuous symmetry transformations, within the framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism, which are over and above the usual off-shell nilpotent and absolutely anticommuting (anti-)BRST transformations that are respected by the quantum version of the classical first-order Lagrangian for the Friedberg-Lee-Pang-Ren (FLPR) model that describes the motion of a single non-relativistic particle of unit mass (moving under the influence of a general rotationally invariant spatial two-dimensional potential). We christen these novel set of fermionic transformations as the (anti-)co-BRST transformations because the gauge-fixing terms remain invariant under them. We derive the conserved and off-shell nilpotent (anti-)BRST and (anti-)co-BRST charges and comment on the physicality criteria with respect to them where we establish the presence of the operator forms of the first-class constraints (of the original classical gauge theory) at the quantum level which is consistent with the Dirac-quantization conditions.