Unambiguous one-loop quantum energies of 1+1 dimensional bosonic field configurations

We calculate one-loop quantum energies in a renormalizable self-interacting theory in one spatial dimension by summing the zero-point energies of small oscillations around a classical field configuration, which need not be a solution of the classical field equations. We unambiguously implement standard perturbative renormalization using phase shifts and the Born approximation. We illustrate our method by calculating the quantum energy of a soliton/antisoliton pair as a function of their separation. This energy includes an imaginary part that gives a quantum decay rate and is associated with a level crossing in the solutions to the classical field equation in the presence of the source that maintains the soliton/antisoliton pair.