Aharonov-Bohm Order Parameters for Non-Abelian Gauge Theories

TL;DR

This paper introduces a new set of Aharonov-Bohm order parameters for non-Abelian gauge theories, addressing previous challenges by unifying test particles in the same measurement setup and emphasizing gauge fixing.

Contribution

It proposes a novel framework for defining order parameters in non-Abelian gauge theories using Aharonov-Bohm effects, overcoming calibration issues in prior methods.

Findings

Order parameters successfully distinguish different gauge symmetry realizations.

Unified test particles improve measurement consistency.

Gauge fixing is crucial for accurate order parameter definition.

Abstract

The Aharonov-Bohm effect has been invoked to probe the phase structure of a gauge theory. Yet in the case of non-Abelian gauge theories, it proves difficult to formulate a general procedure that unambiguously specifies the realization of the gauge symmetry, e.g. the unbroken subgroup. In this paper, we propose a set of order parameters that will do the job. We articulate the fact that any useful Aharonov-Bohm experiment necessarily proceeds in two stages: calibration and measurement. World sheets of virtual cosmic string loops can wrap around test charges, thus changing their states relative to other charges in the universe. Consequently, repeated flux measurements with test charges will not necessarily agree. This was the main stumbling block to previous attempts to construct order parameters for non-Abelian gauge theories. In those works, the particles that one uses for calibration and subsequent measurement are stored in {\em separate} ``boxes''. By storing all test particles in the {\em same} ``box'', we show how quantum fluctuations can be overcome. The importance of gauge fixing is also emphasized.