Nonlocal scalar electrodynamics from Chern-Simons theory

TL;DR

This paper quantizes a complex scalar field coupled to a Chern-Simons gauge field, revealing a nonlocal scalar theory with calculable scattering processes, advancing understanding of topological gauge interactions.

Contribution

It introduces a canonical quantization of scalar-Chern-Simons theory, separating variables gauge-independently and deriving a nonlocal scalar interaction with explicit scattering calculations.

Findings

Reduced to a nonlocal scalar theory in the physical subspace

Calculated scattering cross sections for several processes

Demonstrated gauge-independent variable separation

Abstract

The theory of a complex scalar interacting with a pure Chern-Simons gauge field is quantized canonically. Dynamical and nondynamical variables are separated in a gauge-independent way. In the physical subspace of the full Hilbert space, this theory reduces to a pure scalar theory with nonlocal interaction. Several scattering processes are studied and the cross sections are calculated.