Perturbative expansion of quantum states of extended objects

We construct an effective Hamiltonian at fixed momentum which can be used to calculate higher-order corrections to quantum states of localized classical solutions of scalar field theories in 1 + 1 dimensions. We use the quantization scheme discussed first by Creutz and also by Rothe and one of the present authors (J.B.). The effective Hamiltonian is similar to, but nevertheless different from the one obtained in the collective coordinate method. The agreement of the energy corrections at the two-loop level has been checked.