On the Infrared Limit of Unconstrained SU(2) Yang-Mills Theory

TL;DR

This paper derives an effective nonlinear sigma model for the infrared limit of unconstrained SU(2) Yang-Mills theory using Hamiltonian formalism, connecting it to recent proposals by Faddeev and Niemi.

Contribution

It introduces a new Hamiltonian-based approach to derive the infrared effective Lagrangian for SU(2) Yang-Mills theory, simplifying the physical fields involved.

Findings

Effective nonlinear sigma model Lagrangian derived

Involves only one scalar and two rotational fields

Discusses relation to Faddeev-Niemi Lagrangian

Abstract

The variables appropriate for the infrared limit of unconstrained SU(2) Yang-Mills field theory are obtained in the Hamiltonian formalism. It is shown how in the infrared limit an effective nonlinear sigma model type Lagrangian can be derived which out of the six physical fields involves only one of three scalar fields and two rotational fields summarized in a unit vector. Its possible relation to the effective Lagrangian proposed recently by Faddeev and Niemi is discussed.