UC Santa Cruz

Solitons are a class of solution to equations that appear in the study of physics, particularly the study of fields and field theory. In the study of quantum field theory, solitons often present themselves as heavy degrees of freedom, and are therefore approached from a semi-classical perspective. Traditionally, the soliton is considered as the background field with which perturbative quantum states are defined with respect to. In this dissertation, we present the position that this approach is flawed. In particular, we suggest that using classical solitons as a starting point of analysis only narrowly covers the scope of the possibilities for solitons to manifest in quantum field theories. We show that there are classical solitons of infinite mass which in the quantum theory have their mass rendered finite. We additionally describe circumstances where quantum effects are large enough to significantly alter the net forces which act upon solitons, compared to the classical case. The conclusion is simple: quantum field theory generically contains a much larger space of dynamically accessible field configurations than classical field theory, and this facilitates the existence of quantum solitons that would not exist in the classical case.