Abstract
A rigorous construction of new super-selection selectors — so-called “soliton-sectors” — for the quantum “sine-Gordon” equation and the (φ·φ)2-quantum field models with explicitly broken isospin symmetry in two space-time dimensions is presented. These sectors are eigenspaces of the chargeQ≡∫dx(grad φ)(x) with non-zero eigenvalue. The scattering theory for quantum solitons is briefly discussed and shown to have consequences for the physics in the vacuum sector. A general theory is developed which explains why soliton-sectors may exist for theories in two but not in four space-time dimensions except possibly for non-abelian Yang-Mills theories.
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Communicated by A. S. Wightman
Supported in part by the National Science Foundation under Grant NSF-GP-39048 and by the ETH, Zürich.
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Fröhlich, J. New super-selection sectors (“soliton-states”) in two dimensional Bose quantum field models. Commun.Math. Phys. 47, 269–310 (1976). https://doi.org/10.1007/BF01609844
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DOI: https://doi.org/10.1007/BF01609844