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Regulator dependence in the functional renormalization group: A quantitative explanation.

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Controlled approximations for strongly coupled systems are challenging. This study clarifies how regulator shape impacts derivative expansion convergence within Wilson

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Area of Science:

  • Theoretical physics
  • Quantum field theory
  • Statistical mechanics

Background:

  • Studying strongly coupled systems requires controlled approximations beyond perturbation theory.
  • Wilson's renormalization group (RG) provides a powerful framework for such approximations.
  • The derivative expansion is a widely used approximation scheme within RG.

Purpose of the Study:

  • To investigate the dependence of derivative expansion convergence on regulator shape.
  • To provide a theoretical justification for the principle of minimal sensitivity in fixing this dependence.

Main Methods:

  • Analysis of Wilson's renormalization group framework.
  • Investigation of the derivative expansion approximation scheme.
  • Exploration of regulator functions and their properties.

Main Results:

  • The convergence of the derivative expansion is indeed strongly dependent on the regulator's shape.
  • The study clarifies the underlying reasons for this observed dependence.
  • A justification for the principle of minimal sensitivity is provided.

Conclusions:

  • Understanding regulator dependence is crucial for accurate approximations in strongly coupled systems.
  • The principle of minimal sensitivity offers a robust method for optimizing approximations.
  • This work advances the application of Wilson's RG for complex physical systems.