Properties of derivative expansion approximations to the renormalization group

Abstract

Approximation only by derivative (or more generally momentum) expansions, combined with reparametrization invariance, turns the continuous renormalization group for quantum field theory into a set of partial differential equations which at fixed points become non-linear eigenvalue equations for the anomalous scaling dimension $\eta$. We review how these equations provide a powerful and robust means of discovering and approximating non-perturbative continuum limits. Gauge fields are briefly discussed. Particular emphasis is placed on the rôle of reparametrization invariance, and the convergence of the derivative expansion is addressed.

(Minor touch ups of the lingo.) Invited talk at RG96, Dubna, Russia; 14 pages including 2 eps figures; uses LaTeX, epsf and sprocl.sty

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Cited by in corpus (29)

• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Theory of the Weakly Interacting Bose Gas
• Exact Renormalization Group Equations. An Introductory Review
• Nonperturbative renormalization group approach to frustrated magnets
• Optimization of the derivative expansion in the nonperturbative renormalization group
• Lectures on renormalization and asymptotic safety
• A gauge invariant exact renormalization group I
• Functional Callan-Symanzik equation
• Epsilon Expansion for Multicritical Fixed Points and Exact Renormalisation Group Equations
• Renormalization group methods and the 2PI effective action
• Renormalization-Group Analysis of the Generalized sine-Gordon Model and of the Coulomb Gas for d >= 3 Dimensions
• Application of Renormalization Group Techniques to a Homogeneous Bose Gas at Finite Temperature
• Scaling and superscaling solutions from the functional renormalization group
• Remarks on Exact RG Equations
• Wegner-Houghton equation and derivative expansion
• Truncation Effects in the Functional Renormalization Group Study of Spontaneous Symmetry Breaking
• Renormalization group flow equations connected to the $n$PI effective action
• The fate of non-polynomial interactions in scalar field theory
• Universal behavior of coupled order parameters below three dimensions
• Revisiting the local potential approximation of the exact renormalization group equation
• Reparameterisation Invariance and RG equations: Extension of the Local Potential Approximation
• Renormalization of composite operators
• Stability of fixed points and generalized critical behavior in multifield models
• The epsilon-expansion in the symmetry-broken phase of an interacting Bose gas at finite temperature
• Renormalization group flow equations with full momentum dependence
• Vainshtein in the UV and a Wilsonian analysis of derivatively coupled scalars
• The Universal Equation of State near the Critical Point of QCD
• Maximal Locality and Predictive Power in Higher-Dimensional, Compactified Field Theories
• A functional renormalization method for wave propagation in random media