Exact evolution equation for the effective potential

TL;DR

This paper derives an exact evolution equation for the effective potential, enabling better analysis of infrared problems in theories with massless modes, relevant for phase transitions and critical phenomena.

Contribution

It introduces a new exact evolution equation for the effective action's scale dependence, facilitating improved handling of infrared issues in various physical theories.

Findings

Allows truncation of the evolution equation for practical calculations

Addresses infrared problems in theories with massless modes

Applicable to high temperature phase transitions and critical exponent computations

Abstract

We derive a new exact evolution equation for the scale dependence of an effective action. The corresponding equation for the effective potential permits a useful truncation. This allows one to deal with the infrared problems of theories with massless modes in less than four dimensions which are relevant for the high temperature phase transition in particle physics or the computation of critical exponents in statistical mechanics.