Perturbation theory and renormalisation group equations

Abstract

We discuss the perturbative expansion of several one-loop improved renormalisation group equations. It is shown that in general the integrated renormalisation group flows fail to reproduce perturbation theory beyond one loop.

5 pages, 1 figure, revtex, typos corrected, eq. (19) added, discussion extended, to appear in PRD

References in corpus (16)

• Exact evolution equation for the effective potential
• The Exact Renormalisation Group and Approximate Solutions
• Exact Renormalization Group Equations. An Introductory Review
• Flow Equations for N Point Functions and Bound States
• On the Connection Between Momentum Cutoff and Operator Cutoff Regularizations
• Renormalization Group Flow and Equation of State of Quarks and Mesons
• Towards an accurate determination of the critical exponents with the Renormalization Group flow equations
• Renormalization Group Flow Equations and the Phase Transition in O(N)-models
• Predictive power of renormalisation group flows: a comparison
• Improving the Renormalization Group approach to the quantum-mechanical double well potential
• On the Convergence of the Expansion of Renormalization Group Flow Equation
• Operator Cutoff Regularization and Renormalization Group in Yang-Mills Theory
• Proper time regulator and Renormalization Group flow
• The heat-kernel and the average effective potential
• Renormalization Group Flow Equation at Finite Density
• Renormalization Group Flow in large N_c

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• Finite-Size Scaling behavior in the O(4)-Model
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• Functional Renormalisation for $f(R_{\mu \nu \rho \sigma })$ Quantum Gravity
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• Pressure and speed of sound in two-flavor color-superconducting quark matter at next-to-leading order
• Heat kernel coefficients on the sphere in any dimension
• Effective Action from the Functional Renormalization Group
• Towards Functional Flows for Hierarchical Models
• Enhancement of field renormalization in scalar theories via functional renormalization group
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• Path integral quantization of scalar fluctuations above a kink
• Effect of the quartic gradient terms on the critical exponents of the Wilson-Fisher fixed point in $O(N)$ models
• Subtleties in the calculation of correlation functions for hot and dense systems
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• A renormalization group improved computation of correlation functions in theories with non-trivial phase diagram
• Wilsonian Renormalization Group In The Functional Nonperturbative Approach