Article

The Derivative Expansion of the Effective Action and the Renormalization Group Equation

07/2007;
Source: arXiv

ABSTRACT The perturbative evaluation of the effective action can be expanded in powers of derivatives of the external field. We apply the renormalization group equation to the term in the effective action that is second order in the derivatives of the external field and all orders in a constant external field, considering both massless scalar $\phi_4^4$ model and massless scalar electrodynamics. A so-called ``on shell'' renormalization scheme permits one to express this ``kinetic term'' for the scalar field entirely in terms of the renormalization group functions appropriate for this scheme. These renormalization group functions can be related to those associated with minimal subtraction.

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Keywords

constant external field
 
derivatives
 
effective action
 
external field
 
massless scalar electrodynamics
 
minimal subtraction
 
perturbative evaluation
 
powers
 
renormalization group equation
 
renormalization group functions
 
renormalization group functions appropriate
 
scalar field
 
so-called ``on shell'' renormalization scheme permits