Canonical Quantization of Chern-Simons on the Light-Front

TL;DR

This paper performs canonical quantization of the Abelian Chern-Simons model on the light-front, clarifying debates about anyons and fractional statistics through detailed analysis of constrained systems.

Contribution

It provides a systematic light-front quantization of the Chern-Simons model, addressing controversies and analyzing both scalar and spinor coupled fields.

Findings

Clarifies the relation between fractional spin and statistics in the model

Details the properties of the Chern-Simons theory on the light-front

Uses Dirac's method for constrained systems

Abstract

By performing the canonical quantization of the Abelian Chern-Simons model on the light-front (as suggested by Dirac), we clarify some controversies appearing in recent papers that discuss the relation between the existence of excitations carrying fractional spin and statistics (anyons) and this model. Properties of the Chern-Simons model on the light-front are investigated in detail, following the Dirac method for constrained dynamical systems, both for a coupled complex scalar field as well as for a spinor field.