Unconstrained SU(2) Yang-Mills Quantum Mechanics with Theta Angle

TL;DR

This paper derives and quantizes an unconstrained classical model of SU(2) Yang-Mills theory with a theta angle, solving for low-energy states and analyzing ground state properties, including topological effects.

Contribution

It provides a new unconstrained Hamiltonian formulation of SU(2) Yang-Mills quantum mechanics with theta angle and explores its spectral and topological properties.

Findings

Energy spectrum is independent of the theta angle.

Ground state exhibits specific electric and magnetic properties.

Calculated gluon condensate and topological susceptibility support variational results.

Abstract

The unconstrained classical system equivalent to spatially homogeneous SU(2) Yang-Mills theory with theta angle is obtained and canonically quantized. The Schr\"odinger eigenvalue problem is solved approximately for the low lying states using variational calculation. The properties of the groundstate are discussed, in particular its electric and magnetic properties, and the value of the "gluon condensate" is calculated. Furthermore it is shown that the energy spectrum of SU(2) Yang-Mills quantum mechanics is independent of the theta angle. Explicit evaluation of the Witten formula for the topological susceptibility gives strong support for the consistency of the variational results obtained.