Symplectic structure free Chern-Simons Theory

TL;DR

This paper develops a new formulation of abelian Chern-Simons theory by transforming second class constraints into a first class system, leading to an extended gauge symmetry and a novel action without symplectic structure.

Contribution

It introduces a symplectic structure free Chern-Simons action with an infinite set of irreducible first class constraints and extended gauge symmetries.

Findings

Disappearance of symplectic structure in the new formulation

Introduction of an infinite set of first class constraints

Emergence of extended local gauge symmetries

Abstract

The second class constraints algebra of the abelian Chern-Simons theory is rigorously studied in terms of the Hamiltonian embedding in order to obtain the first class constraint system. The symplectic structure of fields due to the second class constraints disappears in the resulting system. Then we obtain a new type of Chern-Simons action which has an infinite set of the irreducible first class constraints and exhibits new extended local gauge symmetries implemented by these first class constraints.