paper

Aharonov-Bohm Order Parameters for Non-Abelian Gauge Theories

arXiv:hep-th/9502080 · doi:10.1103/PhysRevD.52.7247

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.

How quantum fluctuations destroy the coherence between various strings are discussed explicitly. That linked Wilson loops are useful order parameters for a Maxwell- Chern-Simons-Higgs theory is noted. The generality of our results is emphasized. Problems with figures have also been fixed. 43 pages, 13 figures, Revtex, accepted for publication in PRD

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