Polchinski equation, reparameterization invariance and the derivative expansion

1997/05/19 by Jordi Comellas · 49 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Black Holes and Theoretical Physics #Connection (principal bundle) #Critical dimension #Critical exponent #Dimension (graph theory) #Fixed point #Infinitesimal #Nonlinear Waves and Solitons #Scalar (mathematics) #hep-lat #hep-ph #hep-th

paper · pdf · doi:10.1016/s0550-3213(97)00692-5

published in Nuclear Physics B 509(3), 662-686 (Elsevier BV) · 28 pages, LaTeX with psfig, 12 encapsulated PostScript figures. A number wrongly quoted in the abstract corrected

arxiv created 1997/05/19 · openalex publication_date 1998/01/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The connection between the anomalous dimension and some invariance properties of the fixed point actions within exact RG is explored. As an application, Polchinski equation at next-to-leading order in the derivative expansion is studied. For the Wilson fixed point of the one-component scalar theory in three dimensions we obtain the critical exponents η=0.042, ν=0.622 and ω=0.754.

Citations

• The renormalization group and the ε expansion
• Momentum scale expansion of sharp cutoff flow equations
• O(N) models within the local potential approximation
• Gauge invariance, the quantum action principle, and the renormalization group
• Scheme independence and the exact renormalization group