Symplectic Quantization of the CP$^1$ Model with the Chern-Simons Term

TL;DR

This paper applies the symplectic formalism to analyze the gauge-invariant CP$^1$ model with a Chern-Simons term, effectively incorporating the model's constraints at the Lagrangian level.

Contribution

It introduces a consistent symplectic approach to handle the CP$^1$ constraint in the presence of a Chern-Simons term.

Findings

Successfully incorporated the CP$^1$ constraint at the Lagrangian level.

Provided a gauge-invariant formulation of the model.

Enhanced understanding of the symplectic structure in topological field theories.

Abstract

The symplectic formalism is fully employed to study the gauge-invariant CP$^1$ model with the Chern-Simons term. We consistently accommodate the CP$^1$ constraint at the Lagrangian level according to this formalism.