Abstract
The following two main reasons justify the recent vivid interest in σ-models:
-
i)
In O(N) σ-models (in dimension d = N − 1) and the two-dimensional CP(n) σ-models *) one can introduce the topological quantum numbers and instantons as in four-dimension- al Yang-Mills theories.
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ii)
The classical dynamics of the large class of σ-models (including O(N) and CP(n)) is determined by the presence of an infinite number of conserved nonlocal charges [5–8]. One expects that the formalism of σ-models may provide a hint of how to eventually treat the Yang-Mills theory as a completely integrable four-dimensional system.
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Lukierski, J. (1980). Fourdimensional Quaternionic σ-Models. In: Rühl, W. (eds) Field Theoretical Methods in Particle Physics. NATO Advanced Study Institutes Series, vol 55. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-3722-5_16
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DOI: https://doi.org/10.1007/978-1-4684-3722-5_16
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