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

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 ${\varphi }_4^4$ 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.

arXiv commentLatex; 12 pages; no figure; typos corrected; references revised; journal version

References in corpus (8)

• The effective potential and the renormalisation group
• Renormalization Group Improvement of the Effective Potential in Massive O(N) Symmetric ${\varphi }^4$ Theory
• Five-loop renormalization group functions of $O(n)$-symmetric ${\varphi }^4$-theory and $\ep$-expansions of critical exponents up to $\ep^5$
• Improving the Effective Potential
• Optimal Renormalization-Group Improvement of Two Radiatively-Broken Gauge Theories
• Multi-scale Renormalisation Group Improvement of the Effective Potential
• Renormalization group improvement of the effective potential in massive ${\varphi }^4$ theory
• Higher Order Stability of a Radiatively Induced 220 GeV Higgs Mass

Cited by in corpus (3)

• Can the Renormalization Group Improved Effective Potential be used to estimate the Higgs Mass in the Conformal Limit of the Standard Model?
• Summing Radiative Corrections to the Effective Potential
• The Relationship between Bare and Renormalized Couplings in Scalar Electrodynamics