Abstract
Spontaneous symmetry breaking is studied in the ultralocal limit of a scalar quantum field theory, that is when [Formula: see text] (or infrared limit). In this infrared approximation the theory [Formula: see text] is formally two-dimensional and its Euclidean solutions are instantons. For BPST-like solutions with [Formula: see text], the map between [Formula: see text] in two dimensions and self-dual Yang–Mills theory is carefully discussed.
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