Abstract
In this chapter we study the classical sigma model coupled with a gauge field. Using techniques in nonlinear functional analysis, we are able to establish a precise description of the static solutions in various topological classes. In §2.1 we review the Belavin—Polyakov solution of the classical sigma model. In §2.2 we describe the gauged sigma model and state our existence theorems. In §2.3 we reduce the problem into a semilinear elliptic equation. In §2.4 we present a complete mathematical analysis and prove all the results stated.
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© 2001 Springer Science+Business Media New York
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Yang, Y. (2001). Sigma Models. In: Solitons in Field Theory and Nonlinear Analysis. Springer Monographs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-6548-9_2
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DOI: https://doi.org/10.1007/978-1-4757-6548-9_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-2919-8
Online ISBN: 978-1-4757-6548-9
eBook Packages: Springer Book Archive