Coherent States and a Path Integral for the Relativistic Linear Singular Oscillator

TL;DR

This paper develops a coherent state framework and path integral formulation for a relativistic linear singular oscillator, deriving exact energy spectra and classical equations of motion in a curved phase space.

Contribution

It introduces SU(1,1) coherent states for the relativistic oscillator and derives a path integral approach, providing new insights into its quantization and classical dynamics.

Findings

Exact energy spectrum via Bohr-Sommerfeld quantization

Path integral for transition amplitudes between coherent states

Classical equations of motion in curved phase space

Abstract

The SU(1,1) coherent states for a relativistic model of the linear singular oscillator are considered. The corresponding partition function is evaluated. The path integral for the transition amplitude between SU(1,1) coherent states is given. Classical equations of the motion in the generalized curved phase space are obtained. It is shown that the use of quasiclassical Bohr-Sommerfeld quantization rule yields the exact expression for the energy spectrum.