Chern-Simons vortices in an open system

TL;DR

This paper investigates a gauge invariant quantum field theory with a spacetime dependent Chern-Simons coefficient, revealing how gradients induce magnetic-moment corrections and affect vortex singularities, with implications for Hall current behavior.

Contribution

It introduces a formalism for analyzing Chern-Simons theories with spacetime-dependent coefficients, showing new effects on vortices and Hall currents not previously documented.

Findings

Gradients in the Chern-Simons coefficient induce magnetic-moment corrections.

Vortex singularities become non-local objects due to the coefficient's spacetime dependence.

The fundamental commutator for density fluctuations is derived from the action principle.

Abstract

A gauge invariant quantum field theory with a spacetime dependent Chern-Simons coefficient is studied. Using a constraint formalism together with the Schwinger action principle it is shown that non-zero gradients in the coefficient induce magnetic-moment corrections to the Hall current and transform vortex singularities into non-local objects. The fundamental commutator for the density fluctuations is obtained from the action principle and the Hamiltonian of the Chern-Simons field is shown to vanish only under the restricted class of variations which satisfy the gauge invariance constraint.