Momentum scale expansion of sharp cutoff flow equations

1995/08/31 by Tim R. Morris · 10 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Quantum and Classical Electrodynamics #Theoretical and Computational Physics #cond-mat #hep-lat #hep-ph #hep-th

paper · pdf · doi:10.1016/0550-3213(95)00541-2

published as Nucl.Phys. B458 (1996) 477-503 · 31 pages including 5 eps figures, uses harvmac and epsf. Minor additions -- not worth the bandwidth if you already have a copy

arxiv created 1995/09/07 · openalex publication_date 1996/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We show how the exact renormalization group for the effective action with a sharp momentum cutoff, may be organised by expanding one-particle irreducible parts in terms of homogeneous functions of momenta of integer degree (Taylor expansions not being possible). A systematic series of approximations -- the O(p^M) approximations -- result from discarding from these parts, all terms of higher than the M^{\rm th} degree. These approximations preserve a field reparametrization invariance, ensuring that the field's anomalous dimension is unambiguously determined. The lowest order approximation coincides with the local potential approximation to the Wegner-Houghton equations. We discuss the practical difficulties with extending the approximation beyond O(p⁰).

Citations

• The renormalization group and the ε expansion
• Exact evolution equation for the effective potential
• Critical exponents from the effective average action

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• Dimensional crossover and effective exponents