Conformal Symmetry and Effective Potential: I. Vacuum $V_{z,x}$-operation for the Green functions

Abstract

We begin a series of two papers that is devoted to the study of the multi-loop effective potential evolution in ${\phi }^4$-theory using the conformal symmetry. In the first part, we introduce and describe in detail the vacuum $V_{z,x}$-operation ($"V"$ stems from "vacuum", $\{z,x\}$ imply the corresponding coordinates) that transforms the given Green functions to the corresponding vacuum integrations which generate the effective potential. Our operation can be considered as an inverse procedure compared to the Gorishni-Isaev method. To the final goal, it is necessary to introduce also the special treatment of the mass terms as sorts of "interaction" in an asymptotical expansion of the generating functional.

Comments: 14 pages, 3 figures; the version matches the journal variant