Renormalisation group aided finite temperature reduction of quantum field theories

Abstract Dimensional reduction of finite temperature quantum field theories can be improved with the help of continous renormalisation group steps. The method is applied to the integration of the lowest nonstatic (n=±1) modes of the finite temperatureΦ4-theory. A second, physically important application is the integration of the Debye-screenedA0(x) static scalar potential in the gauged SU(2) Higgs model.