RENORMALISATION GROUP AIDED FINITE TEMPERATURE REDUCTION OF QUANTUM FIELD THEORIES

Dimensional reduction of finite temperature quantum field theories can be improved with help of continous renormalisation group steps. The method is applied to the integration of the lowest non-static ($n=\pm 1$) modes of the finite temperature ${\mathrm{\Phi }}^4$-theory. A second, physically important application is the integration of the Debye-screened ${\mathbf{A}}_{\mathbf{0}}(x)$ static scalar potential in the gauged SU(2) Higgs model.