Conformal symmetry and effective potential: I. Vacuum Vz, x operation for the Green functions

Abstract

Abstract We begin a series of two papers that is devoted to the study of the multi-loop effective potential evolution in φ4 theory using the conformal symmetry. In this first part, we introduce and describe in detail the vacuum Vz, x operation (“V” stems from “vacuum”; {z, x} imply the corresponding coordinates) that transforms the given Green’s functions to the corresponding vacuum integrations that generate the effective potential. Our operation can be considered as an inverse procedure compared to the Gorishnii–Isaev method. To reach the final goal, it is also necessary to introduce a special treatment of the mass terms as types of “interaction” in an asymptotical expansion of the generating functional.