Nonlocal electrodynamics in 2+1 dimensions from Chern-Simons theory

TL;DR

This paper quantizes a spinor field coupled with a Chern-Simons gauge field in 2+1 dimensions, deriving a nonlocal interaction theory and analyzing scattering processes with Lorentz-invariant cross sections.

Contribution

It introduces a gauge-independent quantization method for the theory and derives a nonlocal spinor interaction from Chern-Simons dynamics.

Findings

Derived explicit Lorentz-invariant cross sections for scattering processes

Separated dynamical and nondynamical variables in a gauge-independent manner

Reduced the theory to a pure spinor field with nonlocal interactions

Abstract

The theory of a spinor field interacting with a pure Chern-Simons gauge field in 2+1 dimensions is quantized. Dynamical and nondynamical variables are separated in a gauge-independent way. After the nondynamical variables are dropped, this theory reduces to a pure spinor field theory with nonlocal interaction. Several two-body scattering processes are studied and the cross sections are obtained in explicitly Lorentz invariant forms.