Multi-axion solutions to the strong CP problem produce varied mass-coupling patterns set by PQ symmetry breaking structure and QCD-EM anomaly alignment, summarized by a general sum rule for N-axion systems.
Consequences of the order of
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The ACGT order-of-limits prescription fails to reproduce the correct θ-dependent energy spectrum in the quantum rotor and quantum pendulum.
The θ-vacuum structure in QCD produces observable CP violation when the theory is consistently quantized with boundary degrees of freedom accounted for in the infinite-volume limit.
CP conservation in QCD follows from taking the infinite volume limit prior to summing over topological sectors, shown consistent with steepest-descent contours and chiral EFT.
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A particle on a ring or: how I learned to stop worrying and love $\theta$-vacua
The ACGT order-of-limits prescription fails to reproduce the correct θ-dependent energy spectrum in the quantum rotor and quantum pendulum.