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We consider the semiclassical quantization of sine-Gordon solitons on thecircle with periodic and anti-periodic boundary conditions. The 1-loop quantumcorrections to the mass of the solitons are determined using zeta functionregularization in the integral representation. We compare the semiclassicalresults with exact numerical calculations in the literature and find excellentagreement even outside the plain semiclassical regime.

Quantization of Sine-Gordon solitons on the circle: semiclassical vs. exact results