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