Theta terms and asymptotic behavior of gauge potentials in (3+1) dimensions

TL;DR

This paper explores how certain gauge configurations in (3+1)D QED influence the quantum phase through the theta angle, highlighting configurations with specific asymptotic behaviors related to magnetic helicity and Chern-Simons number.

Contribution

It identifies gauge potentials with slow fall-off behavior that affect the quantum phase via the theta angle, linking topological properties to physical configurations.

Findings

Configurations with gauge potentials falling off as 1/r influence the phase.

Relative phase depends on theta times the difference in Chern-Simons number.

Implications for QCD and the strong CP problem are discussed.

Abstract

We describe paths in the configuration space of (3+1) dimensional QED whose relative quantum phase (or relative phase in the functional integral) depends on the value of the theta angle. The final configurations on the two paths are related by a gauge transformation but differ in magnetic helicity or Chern-Simons number. Such configurations must exhibit gauge potentials that fall off no faster than 1/r in some region of finite solid angle, although they need not have net magnetic charge (i.e., are not magnetic monopoles). The relative phase is proportional to theta times the difference in Chern-Simons number. We briefly discuss some possible implications for QCD and the strong CP problem.