One Loop Renormalization of Soliton Quantum Mass Corrections in 1+1 Dimensional Scalar Field Theory Models

The bare one loop soliton quantum mass corrections can be expressed in two ways: as a sum over the zero-point energies of small oscillations around the classical configuration, or equivalently as the (Euclidean) effective action per unit time. In order to regularize the bare one loop quantum corrections (expressed as the sum over the zero-point energies) we subtract and add from it the tadpole graph that appear in the expansion of the effective action per unit time. The subtraction renders the one loop quantum corrections finite. Next, we use the renormalization prescription that the added tadpole graph cancels with adequate counterterms, obtaining in this way a finite unambiguous expression for the one loop soliton quantum mass corrections. When we apply the method to the solitons of the sine-Gordon and $\phi^4$ kink models we obtain results that agree with known results. Finally we apply the method to compute the soliton quantum mass corrections in the recently introduced $\phi^2\cos^2\ln(\phi^2)$ model