Perturbative Renormalizations of Anyon Quantum Mechanics

TL;DR

This paper investigates regularization and renormalization techniques in bosonic end perturbative calculations for anyon quantum mechanics, clarifying their physical meaning and applying them to derive spectral results like the 3-anyon ground state energy.

Contribution

It evaluates the reliability of common regularization methods and introduces a physically transparent approach to derive perturbative spectra for anyon systems.

Findings

Validated a regularization procedure with clear physical interpretation

Derived perturbative results for anyon spectra including the 3-anyon ground state energy

Clarified the physical meaning of regularization in anyon quantum mechanics

Abstract

In bosonic end perturbative calculations for quantum mechanical anyon systems a regularization and renormalization procedure, analogous to those used in field theory, is necessary. I examine the reliability and the physical interpretation of the most commonly used bosonic end regularization procedures. I then use the regularization procedure with the most transparent physical interpretation to derive some bosonic end perturbation theory results on anyon spectra, including a 3-anyon ground state energy.