Path integral quantization of scalar fluctuations above a kink

We quantize scalar fluctuations in 1+1 dimensions above a classical background kink. The properties of the effective action for the corresponding classical field are studied with an exact functional method, alternative to exact Wilsonian renormalization, where the running parameter is a bare mass, and the regulator of the quantum theory is fixed. We extend this approach, in an appendix, to a Yukawa interaction in higher dimension.