Conformal anomaly in non-hermitian quantum mechanics

TL;DR

This paper investigates a non-Hermitian, PT-symmetric quantum system involving an electron and monopole, revealing how anomalous scale symmetry breaking leads to wave-packet localization and complex symmetry algebra structures.

Contribution

It introduces a detailed model of a PT-symmetric non-Hermitian system with analysis of its conformal symmetry and algebraic structure, highlighting novel symmetry properties.

Findings

Wave-packet localization due to anomalous scale symmetry breaking

Conformal algebra SO(2,1) belongs to the enveloping algebra of combined Virasoro and abelian algebras

Identification of the symmetry algebra structure in the non-Hermitian system

Abstract

A model of an electron and a Dirac monopole interacting through an axially symmetric non-hermitian but \mathcal{PT}-symmetric potential is discussed in detail. The intriguing localization of the wave-packet as a result of the anomalous breaking of the scale symmetry is shown to provide a scale for the system. The symmetry algebra for the system, which is the conformal algebra SO(2,1), is discussed and is shown to belong to the enveloping algebra of the combined algebra, composed of the Virosoro algebra, \{L_n, n\in \mathbb{N}\} and an abelian algebra, \{P_n,n\in \mathbb{N}\}.