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Equality and separability in gauge theoriesDebates over the interpretation of gauge theories often take the main choice to be between fiber bundles and holonomies. But this is not the only choice, and focus on this distinction has obscured others. A more important choice is between a “localized gauge properties interpretation” and a “non-localized gauge properties interpretation”, to use Healey’s (2007, 55) terminology. Healey’s holonomy interpretation of classical gauge theories avowedly non-localized, as evidenced by its nonseparability—a striking metaphysical consequence. However, his quantum holonomy interpretation is obtained from a localized, separable classical interpretation. And there is good reason to think that any adequate quantum holonomy interpretation must come from a localized classical interpretation. Given the primacy of the quantum in our investigation of gauge theories, we should reject the non-localized holonomy interpretation and nonseparability along with it.
University of California, San Diego