Batalin-Fradkin-Vilkovisky Quantization and Symmetries of FLPR model

TL;DR

This paper quantizes the FLPR model within the BFV-BRST framework in both polar and Cartesian coordinates using admissible gauge fixing. It constructs nilpotent BRST charges from the first-class constraints, derives BRST-invariant gauge-fixed actions, and verifies physicality criteria consistent with Dirac quantization. Additionally, it develops finite field-dependent BRST (FFBRST) transformations to relate the BFV gauge-fixed action to the classical gauge-invariant action, demonstrating a controlled connection between quantum and classical descriptions. The results establish a coherent BRST quantization for the FLPR system, with cross-coordinate consistency and FFBRST mappings that address gauge-fixed versus gauge-invariant formulations.

Abstract

We quantize the Friedberg-Lee-Pang-Ren (FLPR) model within the framework of Batalin-Fradkin-Vilkovisky (BFV) formalism. We construct the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) charges using constraints and the fermionic gauge-fixing function by means of admissible gauge conditions. We also derive the BRST invariant effective action (and corresponding symmetries) of the model in both polar and Cartesian coordinates. We demonstrate that the physical states of the system are annihilated by the first-class constraints which is consistent with the Dirac formalism. Moreover, we establish the finite field-dependent BRST (FFBRST) symmetries of the FLPR model. We exhibit the interlink between the BFV-BRST gauge-fixed action and the classical gauge invariant action using FFBRST formulation.