St\"uckelberg Field Shiftting Quantization of Free-Particle on D-Dimensional Sphere

TL;DR

This paper presents a method for quantizing a free particle on a D-dimensional sphere using St"uckelberg field shifting, demonstrating equivalence to BFFT, and showing the energy spectrum matches the Laplace-Beltrami operator.

Contribution

It introduces a novel quantization approach for particles on curved spaces and establishes its equivalence to existing methods, ensuring consistent energy spectra.

Findings

Quantization via St"uckelberg field shifting is unambiguous.

The method is equivalent to BFFT constraint conversion.

Energy spectrum matches the Laplace-Beltrami operator.

Abstract

In this paper we quantize the free-particle on a D-dimensional sphere in an unambiguous way by converting the second-class constraint using St\"uckelberg field shiftting formalism. Further, we argument that this formalism is equivalent to the BFFT constraint conversion method and show that the energy spectrum is identical to the pure Laplace-Beltrami operator without additional terms arising from the curvature of the sphere. We work out the gauge symmetry generators with results consistent with those obtained through the nonlinear implementation of the gauge symmetry