On Unconstrained SU(2) Gluodynamics with Theta Angle

TL;DR

This paper extends the Hamiltonian reduction of SU(2) Yang-Mills theory to include nonzero theta angles, resulting in a gauge-invariant, unconstrained, nonlocal theory of tensor fields that remains canonically equivalent across different theta values.

Contribution

It generalizes the Hamiltonian reduction process to nonvanishing theta angles, revealing a consistent unconstrained formulation of SU(2) gluodynamics.

Findings

Unconstrained nonlocal theory of tensor fields derived for all theta angles

Canonical equivalence of theories with different theta angles

Extension of Hamiltonian reduction to include theta term

Abstract

The Hamiltonian reduction of classical SU(2) Yang-Mills field theory to the equivalent unconstrained theory of gauge invariant local dynamical variables is generalized to the case of nonvanishing theta angle. It is shown that for any theta angle the elimination of the pure gauge degrees of freedom leads to a corresponding unconstrained nonlocal theory of self-interacting second rank symmetric tensor fields, and that the obtained classical unconstrained gluodynamics with different theta angles are canonically equivalent as on the original constrained level.