Vacuum Periodicity in a Yang-Mills Quantum Theory

We propose a description of the vacuum in Yang-Mills theory and arrive at a physical interpretation of the pseudoparticle solution and the attendant violation of symmetries. The existence of topologically inequivalent classical gauge fields gives rise to a family of quantum mechanical vacua, parametrized by a $\mathrm{CP}$-nonconserving angle. The requirement of vacuum stability against gauge transformations renders the vacua chirally noninvariant.

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