An Extended Soliton's Zero Modes

Quantum field theory in the presence of localized solitons is more complicated than vacuum sector quantum field theory, largely as a result of the soliton’s zero modes. In the present work, we try to understand to what extent this situation carries over to extended solitons. To this end, we explicitly construct the quantum state corresponding to a domain wall string or membrane, treating the zero modes carefully. This is done both for compact and also infinitely extended solitons. As an application, we calculate the differential probability for a domain wall string’s translation mode, with a given momentum, to be excited by a single quantum of incoming radiation.