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Non-integrable aspects of the multi-frequency sine-Gordon model. (English) Zbl 0921.35148
Summary: We consider the two-dimensional quantum field theory of a scalar field self-interacting via two periodic terms of frequencies \(\alpha{}\) and \(\beta{}\). Looking at the theory as a perturbed sine-Gordon model, we use form factor perturbation theory to analyse the evolution of the spectrum of particle excitations. We show how, within this formalism, the non-locality of the perturbation with respect to the solitons is responsible for their confinement in the perturbed theory. The effects of the frequency ratio \(\alpha/\beta\) being a rational or irrational number and the occurrence of massless flows from the Gaussian to the Ising fixed point are also discussed. A generalisation of the Ashkin-Teller model and the massive Schwinger model are presented as examples of application of the formalism.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
81T10 Model quantum field theories
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