Consistent Quantum Expansion Around Soliton Solutions

Abstract

I show that a standard application of the semiclassical techniques to 1+1 dimensional field theories, as originally discussed by Dashen, Hasslacher and Neveu, explicitly violates the Poincare algebra. This problem is traced to the incorrect regularization of the ultraviolet divergences and can be resolved by using a different regularization. I further show that in the case of the doublet solutions in the sine-Gordon theory the semiclassical treatment given by Dashen, Hasslacher and Neveu leads to ambiguous results which depend on the choice of the renormalization counterterm. I discuss a consistent weak coupling expansion which does not suffer from this problem.