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Title: Physics and the choice of regulators in functional renormalisation group flows

Abstract

The Renormalisation Group is a versatile tool for the study of many systems where scale-dependent behaviour is important. Its functional formulation can be cast into the form of an exact flow equation for the scale-dependent effective action in the presence of an infrared regularisation. The functional RG flow for the scale-dependent effective action depends explicitly on the choice of regulator, while the physics does not. In this work, we systematically investigate three key aspects of how the regulator choice affects RG flows: (i) We study flow trajectories along closed loops in the space of action functionals varying both, the regulator scale and shape function. Such a flow does not vanish in the presence of truncations. Based on a definition of the length of an RG trajectory, we suggest a constructive procedure for devising optimised regularisation schemes within a truncation. (ii) In systems with various field variables, a choice of relative cutoff scales is required. At the example of relativistic bosonic two-field models, we study the impact of this choice as well as its truncation dependence. We show that a crossover between different universality classes can be induced and conclude that the relative cutoff scale has to be chosen carefully formore » a reliable description of a physical system. (iii) Non-relativistic continuum models of coupled fermionic and bosonic fields exhibit also dependencies on relative cutoff scales and regulator shapes. At the example of the Fermi polaron problem in three spatial dimensions, we illustrate such dependencies and show how they can be interpreted in physical terms. - Highlights: • We show the regulator dependence of functional renormalisation (FRG) group equations. • Solving FRG equations along closed loops provides a distance between two regulators. • We suggest a practical procedure for devising optimal regulators. • A universality class crossover can be induced by changing relative cutoff scales. • We examine the regulator dependence explicitly in the Fermi polaron problem.« less

Authors:
 [1];  [1];  [2]
  1. Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg (Germany)
  2. ITAMP, Harvard–Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States)
Publication Date:
OSTI Identifier:
22701533
Resource Type:
Journal Article
Journal Name:
Annals of Physics
Additional Journal Information:
Journal Volume: 384; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACTION INTEGRAL; FUNCTIONALS; RELATIVISTIC RANGE; RENORMALIZATION

Citation Formats

Pawlowski, Jan M., ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung mbH, Planckstr. 1, D-64291 Darmstadt, Scherer, Michael M., Schmidt, Richard, Physics Department, Harvard University, 17 Oxford Street, Cambridge, MA 02138, and Wetzel, Sebastian J., E-mail: wetzel_s@thphys.uni-heidelberg.de. Physics and the choice of regulators in functional renormalisation group flows. United States: N. p., 2017. Web. doi:10.1016/J.AOP.2017.06.017.
Pawlowski, Jan M., ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung mbH, Planckstr. 1, D-64291 Darmstadt, Scherer, Michael M., Schmidt, Richard, Physics Department, Harvard University, 17 Oxford Street, Cambridge, MA 02138, & Wetzel, Sebastian J., E-mail: wetzel_s@thphys.uni-heidelberg.de. Physics and the choice of regulators in functional renormalisation group flows. United States. doi:10.1016/J.AOP.2017.06.017.
Pawlowski, Jan M., ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung mbH, Planckstr. 1, D-64291 Darmstadt, Scherer, Michael M., Schmidt, Richard, Physics Department, Harvard University, 17 Oxford Street, Cambridge, MA 02138, and Wetzel, Sebastian J., E-mail: wetzel_s@thphys.uni-heidelberg.de. Fri . "Physics and the choice of regulators in functional renormalisation group flows". United States. doi:10.1016/J.AOP.2017.06.017.
@article{osti_22701533,
title = {Physics and the choice of regulators in functional renormalisation group flows},
author = {Pawlowski, Jan M. and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung mbH, Planckstr. 1, D-64291 Darmstadt and Scherer, Michael M. and Schmidt, Richard and Physics Department, Harvard University, 17 Oxford Street, Cambridge, MA 02138 and Wetzel, Sebastian J., E-mail: wetzel_s@thphys.uni-heidelberg.de},
abstractNote = {The Renormalisation Group is a versatile tool for the study of many systems where scale-dependent behaviour is important. Its functional formulation can be cast into the form of an exact flow equation for the scale-dependent effective action in the presence of an infrared regularisation. The functional RG flow for the scale-dependent effective action depends explicitly on the choice of regulator, while the physics does not. In this work, we systematically investigate three key aspects of how the regulator choice affects RG flows: (i) We study flow trajectories along closed loops in the space of action functionals varying both, the regulator scale and shape function. Such a flow does not vanish in the presence of truncations. Based on a definition of the length of an RG trajectory, we suggest a constructive procedure for devising optimised regularisation schemes within a truncation. (ii) In systems with various field variables, a choice of relative cutoff scales is required. At the example of relativistic bosonic two-field models, we study the impact of this choice as well as its truncation dependence. We show that a crossover between different universality classes can be induced and conclude that the relative cutoff scale has to be chosen carefully for a reliable description of a physical system. (iii) Non-relativistic continuum models of coupled fermionic and bosonic fields exhibit also dependencies on relative cutoff scales and regulator shapes. At the example of the Fermi polaron problem in three spatial dimensions, we illustrate such dependencies and show how they can be interpreted in physical terms. - Highlights: • We show the regulator dependence of functional renormalisation (FRG) group equations. • Solving FRG equations along closed loops provides a distance between two regulators. • We suggest a practical procedure for devising optimal regulators. • A universality class crossover can be induced by changing relative cutoff scales. • We examine the regulator dependence explicitly in the Fermi polaron problem.},
doi = {10.1016/J.AOP.2017.06.017},
journal = {Annals of Physics},
issn = {0003-4916},
number = ,
volume = 384,
place = {United States},
year = {2017},
month = {9}
}