Dougherty, John
(2019)
Sizing up gauge.
In: UNSPECIFIED.
Abstract
Gauge theories feature a distinction between "large" and "small" gauge transformations. Small gauge transformations are said to relate two models representing the same physical state, while large gauge transformations are said to relate distinct physical states of affairs that agree on some or all observables---i.e., to be physical symmetries. This size distinction has real physical consequences, but its conceptual status is obscure. Indeed, it seems to be a hypothesis independent of the rest of quantum field theory, though various plausibility arguments for it do exist. In this paper I offer a conceptual justification of the size distinction on the basis of gauge invariance: in a theory with nontrivial gauge transformations, imposing boundary conditions in a gauge-invariant way produces the size distinction. The landscape of gauge theories is therefore richer than it is often taken to be. Two theories can both deny that gauge transformations are physical symmetries without agreeing on all of the gauge-theoretic facts.
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