Rigorous derivation shows the physical gauge group of Yang-Mills theory is G^I / G^∞_0 for Abelian and non-Abelian cases, following from instantaneous state space structure, with extensions to Yang-Mills-Higgs distinguishing unbroken and broken phases.
Healey, Gauging What’s Real: The Conceptual Foundations of Contemporary Gauge Theories
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Global Gauge Symmetries and Spatial Asymptotic Boundary Conditions in Yang-Mills theory
Rigorous derivation shows the physical gauge group of Yang-Mills theory is G^I / G^∞_0 for Abelian and non-Abelian cases, following from instantaneous state space structure, with extensions to Yang-Mills-Higgs distinguishing unbroken and broken phases.