Exact renormalization group flow equations for free energies and N-point functions in uniform external fields

Abstract

We project the Wilson/Polchinski renormalization group equation onto its uniform external field dependent effective free energy and connected Green's functions. The result is a hierarchy of equations which admits a choice of "natural" truncation and closure schemes for nonperturbative approximate solution. In this way approximation schemes can be generated which avoid power series expansions in either fields or momenta. When following one closure scheme the lowest order equation is the mean field approximation, while another closure scheme gives the "local potential approximation." Extension of these closure schemes to higher orders leads to interesting new questions regarding truncation schemes and the convergence of nonperturbative approximations. One scheme, based on a novel "momentum cluster decomposition" of the connected Green's functions, seems to offer new possibilities for accurate nonperturbative successive approximation.

21 pages, LaTeX; citation clarified, corrected Section 4 material on continuum limit, simplified Section 6 notation

References in corpus (3)

• Nonperturbative Flow Equations, Low-Energy QCD and the Chiral Phase Transition
• Approximate solutions in scalar and fermionic theories within the exact renormalization group approach
• Exact Renormalization Group with Fermions

Cited by in corpus (5)

• Exact Renormalization Group Equations. An Introductory Review
• A new method to solve the Non Perturbative Renormalization Group equations
• Non-Perturbative Renormalization Group calculation of the scalar self-energy
• Wilson-Polchinski exact renormalization group equation for O(N) systems: Leading and next-to-leading orders in the derivative expansion
• Renormalization Group Analysis of Turbulent Hydrodynamics