Momentum Scale Expansion of Sharp Cutoff Flow Equations

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 $M^{\mathrm{th}}$ 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 $O(p^0)$.

31 pages including 5 eps figures, uses harvmac and epsf. Minor additions -- not worth the bandwidth if you already have a copy

References in corpus (3)

• Exact evolution equation for the effective potential
• Scheme Independence and the Exact Renormalization Group
• Stability of Fine Tuned Hierarchies in Strongly Coupled Chiral Models

Cited by in corpus (46)

• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Exact Renormalization Group Equations. An Introductory Review
• Fundamentals of the Exact Renormalization Group
• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• A gauge invariant exact renormalization group I
• Derivative expansion of the renormalization group in O(N) scalar field theory
• Gauge Invariance, the Quantum Action Principle, and the Renormalization Group
• Three dimensional massive scalar field theory and the derivative expansion of the renormalization group
• Large N and the renormalization group
• O(N) models within the local potential approximation
• On the Fixed-Point Structure of Scalar Fields
• Asymptotic safety of simple Yukawa systems
• Equivalence of Local Potential Approximations
• Polchinski equation, reparameterization invariance and the derivative expansion
• A proposal for a manifestly gauge invariant and universal calculus in Yang-Mills theory
• The Electroweak Phase Transition through the Renormalization Group
• Exact scheme independence at two loops
• Wilson Renormalization Group formulation of Real Time thermal field theories
• Exact scheme independence at one loop
• Wilson Renormalization Group Study of Inverse Symmetry Breaking
• Critical behavior of weakly interacting bosons: A functional renormalization group approach
• Properties of derivative expansion approximations to the renormalization group
• Global Renormalization Group
• Two-loop beta-function from the exact renormalization group
• Functional renormalisation group for two-body scattering
• Dimensional Crossover and Effective Exponents
• Exact renormalization group equations and the field theoretical approach to critical phenomena
• Wegner-Houghton equation and derivative expansion
• C Function Representation of the Local Potential Approximation
• Perturbative and non-perturbative aspects of the proper time renormalization group
• The fate of non-polynomial interactions in scalar field theory
• Exact renormalization group study of fermionic theories
• Revisiting the local potential approximation of the exact renormalization group equation
• Convergence of derivative expansions in scalar field theory
• A new universality class describes Vicsek's flocking phase in physical dimensions
• Novel critical phenomena in compressible polar active fluids: Dynamical and Functional Renormalization Group Studies
• Renormalization group and Fermi liquid theory for many-nucleon systems
• Solving the QCD non-perturbative flow equation as a partial differential equation and its application to the dynamical chiral symmetry breaking
• Renormalization Group in Quantum Mechanics
• Renormalization Group Flow Equations for the Sigma Model
• Exact renormalization group approach in scalar and fermionic theories
• Universality in nontrivial continuum limits: a model calculation
• Feynman diagrams with the effective action
• Universal scaling dimensions for highly irrelevant operators in the Local Potential Approximation
• Universality in the exact renormalization group: comparison to perturbation theory
• Momentum-dependence in the infinitesimal Wilsonian renormalization group