Deformed Chern-Simons interaction for nonrelativistic point particles

TL;DR

This paper introduces a deformation of the Chern-Simons interaction for nonrelativistic particles that maintains invariance under area-preserving diffeomorphisms, leading to novel quantum effects and a modified Schrödinger equation.

Contribution

It develops a deformed interaction model with a classical Seiberg-Witten map, resulting in a Schrödinger equation with a singular metric and potential, revealing new quantum phenomena.

Findings

Plane splits into interior and exterior regions due to singular metric

Quantum corrections introduce singularities at the origin and edge of the bag

Solutions of the radial Schrödinger equation exhibit unique properties

Abstract

We deform the interaction between nonrelativistic point particles on a plane and a Chern-Simons field to obtain an action invariant with respect to time-dependent area-preserving diffeomorphisms. The deformed and undeformed Lagrangians are connected by a point transformation leading to a classical Seiberg-Witten map between the corresponding gauge fields. The Schroedinger equation derived by means of Moyal-Weyl quantization from the effective two-particle interaction exhibits - a singular metric, leading to a splitting of the plane into an interior (bag-) and an exterior region, - a singular potential (quantum correction) with singularities located at the origin and at the edge of the bag. We list some properties of the solutions of the radial Schroedinger equation.