We show that large n-particle production rates derived in the semiclassical Higgsplosion limit of scalar field theoretical models with spontaneous symmetry breaking, are consistent with general principles of localizable quantum field theory. The strict localizability criteria of Jaffe defines quantum fields as operator-valued distributions acting on test functions that are localized in finite regions of space–time. The requirement of finite support of test functions in space–time ensures the causality property of QFT. The corresponding localizable fields need not be tempered distributions, and they fit well into the framework of local quantum field theory.
Khoze, V. V., & Spannowsky, M. (2019). Consistency of Higgsplosion in localizable QFT. Physics Letters B, 790, 466-474. https://doi.org/10.1016/j.physletb.2019.01.052