Nonperturbative Aspects of Spontaneous Symmetry Breaking

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 infrared approximation the theory φ4 is formally two-dimensional and its Euclidean solutions are instantons. For BPST-like solutions with Aμa = A μa(x2), the map between φ4 in two dimensions and self-dual Yang-Mills theory is carefully discussed. © 2021 World Scientific Publishing Company.