Perturbative Bosonic End Anyon Spectra and Contact Interactions

TL;DR

This paper introduces a regularization method using delta-function potentials for bosonic end perturbation theory in quantum anyon systems, validating it against known solutions and applying it to explore conjectures about many-anyon spectra.

Contribution

It proposes and verifies a delta-function regularization technique for bosonic end perturbation theory in quantum anyon systems, enabling analysis of complex spectra.

Findings

Regularization matches known two-anyon solutions

Method tests conjectures on many-anyon spectra

Provides a new approach for perturbative calculations

Abstract

Bosonic end perturbative calculations for quantum mechanical anyon systems require a regularization. I regularize by adding a specific $\delta$-function potential to the Hamiltonian. The reliability of this regularization procedure is verified by comparing its results for the 2-anyon in harmonic potential system with the known exact solutions. I then use the $\delta$-function regularized bosonic end perturbation theory to test some recent conjectures concerning the unknown portion of the many-anyon spectra.