Non-Perturbative Renormalization Group calculation of the scalar self-energy

Abstract

We present the first numerical application of a method that we have recently proposed to solve the Non Perturbative Renormalization Group equations and obtain the n-point functions for arbitrary external momenta. This method leads to flow equations for the n-point functions which are also differential equations with respect to a constant background field. This makes them, a priori, difficult to solve. However, we demonstrate in this paper that, within a simple approximation which turns out to be quite accurate, the solution of these flow equations is not more complicated than that of the flow equations obtained in the derivative expansion. Thus, with a numerical effort comparable to that involved in the derivative expansion, we can get the full momentum dependence of the n-point functions. The method is applied, in its leading order, to the calculation of the self-energy in a 3-dimensional scalar field theory, at criticality. Accurate results are obtained over the entire range of momenta.

arXiv comment29 pages

References in corpus (27)

• Exact evolution equation for the effective potential
• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• The Exact Renormalisation Group and Approximate Solutions
• Critical Exponents of the N-vector model
• Optimisation of the exact renormalisation group
• Exact Renormalization Group Equations. An Introductory Review
• Critical Exponents from the Effective Average Action
• Flow Equations for N Point Functions and Bound States
• Derivative Expansion of the Exact Renormalization Group
• The transition temperature of the dilute interacting Bose gas
• Nonperturbative renormalization group approach to frustrated magnets
• Optimization of the derivative expansion in the nonperturbative renormalization group
• Nonperturbative renormalization group approach to the Ising model: a derivative expansion at order ${\partial }^4$
• A new method to solve the Non Perturbative Renormalization Group equations
• Nonperturbative Renormalization Flow and Essential Scaling for the Kosterlitz-Thouless Transition
• Scheme Independence and the Exact Renormalization Group
• Derivative expansion and renormalisation group flows
• Analytical Solutions of Exact Renormalization Group Equations
• Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Seven Loops
• Non perturbative renormalisation group and momentum dependence of $n$-point functions (I)
• Critical equation of state from the average action
• Non perturbative renormalization group and momentum dependence of n-point functions (II)
• Polchinski equation, reparameterization invariance and the derivative expansion
• Critical Phenomena in Continuous Dimension
• Monte Carlo studies of three-dimensional O(1) and O(4) \boldmath{${\varphi }^4$} theory related to BEC phase transition temperatures
• Non Perturbative Renormalization Group, momentum dependence of $n$-point functions and the transition temperature of the weakly interacting Bose gas
• Exact renormalization group flow equations for free energies and N-point functions in uniform external fields

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• The nonperturbative functional renormalization group and its applications
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• Solutions of renormalization group flow equations with full momentum dependence
• Analytic continuation of functional renormalization group equations
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• Non-perturbative renormalization-group approach to lattice models
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• The inviscid fixed point of the multi-dimensional Burgers-KPZ equation
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