QED with massless fermions on a circle (0{≤}x<L) is exactly solved. The nonintegrable phase exp[ie F₀Ldx A₁(t,x)], which is a dynamical degree of freedom on a circle, couples through the anomaly to the zero mode of the fermion-antifermion bound states, leading to the {θ} vacuum.
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Hetrick et al. (1988) studied this question.
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