  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.
