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Geometrical phases and quantum numbers of solitons in nonlinear sigma-models

A. G. Abanov·P. B. Wiegmann
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Abstract

Solitons of a nonlinear field interacting with fermions often acquire a fermionic number or an electric charge if fermions carry a charge. We show how the same mechanism (chiral anomaly) gives solitons statistical and rotational properties of fermions. These properties are encoded in a geometrical phase, i.e., an imaginary part of a Euclidian action for a nonlinear sigma-model. In the most interesting cases the geometrical phase is non-perturbative and has a form of an integer-valued theta-term.

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A. G. Abanov, P. B. Wiegmann. 2001-05-22. Geometrical phases and quantum numbers of solitons in nonlinear sigma-models. https://doi.org/10.1088/1126-6708%2F2001%2F10%2F030

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