A Coherent State Path Integral for Anyons
J. Grundberg, T. H. Hansson
TL;DR
This paper develops an $su(1,1)$ coherent state path integral for two anyons in a harmonic potential, transforming it into a shifted harmonic oscillator integral, and justifies the method via a Holstein-Primakoff transformation analogy.
Contribution
It introduces a novel $su(1,1)$ coherent state path integral formulation for anyons, linking it to a shifted harmonic oscillator through a change of variables.
Findings
Derived a coherent state path integral for anyons in a harmonic potential.
Connected the integral to a shifted harmonic oscillator via variable transformation.
Validated the approach using an $su(1,1)$ Holstein-Primakoff transformation analogy.
Abstract
We derive an coherent state path integral formula for a system of two one-dimensional anyons in a harmonic potential. By a change of variables we transform this integral into a coherent states path integral for a harmonic oscillator with a shifted energy. The shift is the same as the one obtained for anyons by other methods. We justify the procedure by showing that the change of variables corresponds to a version of the Holstein-Primakoff transformation.
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