Scalar Soliton Quantization with Generic Moduli

Abstract

We canonically quantize multi-component scalar field theories in the presence of solitons. This extends results of Tomboulis to general soliton moduli spaces. We derive the quantum Hamiltonian, discuss reparameterization invariance and explicitly show how, in the semiclassical approximation, the dynamics of the full theory reduce to quantum mechanics on the soliton moduli space. We emphasize the difference between the semiclassical approximation and a truncation of the dynamical variables to moduli. Both procedures produce quantum mechanics on moduli space, but the two Hamiltonians are generically different.