Non-Perturbative Aspects of Spontaneous Symmetry Breaking
Abstract
Spontaneous symmetry breaking is studied in the ultralocal limit of a scalar quantum field theory, that is when E≈ m (or infrared limit). In this limit we show that a 4 theory in the euclidean space in four-dimensions describes naturally instantons. Furthermore, in the infrared limit we show that there is an exact map between 4 with self-dual Yang-Mills theories. The spontaneous symmetry breaking in the infrared limit for a Higgs portal is also considered and we demonstrate how states of higher energy becomes unstable and spread converting a false vacuum in a true one.
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