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Introduction to the functional renormalisation group and selected applications

Jan Martin Pawlowski, summer term 2026


Lectures: Monday & Wednesday 11:15-13:00 , SR 106 Pw 12 [HeiCO]


Tutorial: Monday 16:15-18:00, kHS 221 Pw 12 [HeiCO]

Tutor: Konrad Kockler



Prerequisites: Theoretical Physics I-IV, QFT, basic knowledge of renormalisation


Content of lecture series

The lecture course provides an introduction to the functional renormalisation group. The applications deal with modern conceptual developments based on generalised flow equations. Applications of the latter developments is the physics of emergent phenomena such as the formation of bound states and condensation phenomena, and the construction of generative sampling methods for the sampling of lattice theories with and without sign problems.

    Outline

  • The Functional RG


    • Euclidean QFT

    • Functional Renormalisation Group

    • Critical Phenomena & Fixed Points

  • Selected applications


    • Generalised renormalisation group equations and reparameterisations

    • Emergent composites: bound states and condensation phenomena

    • Physics-informed renormalisation group flows

    • The essential renormalisation group

    • Machine Learning, generative architectures and the renormalisation group

Literature

  • Comprehensive review on the fRG

    •   Dupuis, Canet, Eichhorn, Metzner, Pawlowski, Tissier, Wschebor The nonperturbative functional renormalization group and its applications Phys.Rept. 910 (2021) 1-114

  • Introductory reviews on the fRG

    • Aoki Introduction to the Non-perturbative RG Int.J.Mod.Phys.B14:1249-1326,2000
      Berges, Tetradis, Wetterich Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics Phys.Rept.363:223-386,2002
      Polonyi Lectures on the functional renormalization group method Central Eur.J.Phys.1:1-71,2003
      Delamotte An Introduction to the Nonperturbative Renormalization Group Condensed Matter Phys. 8 (2005) 163-179

  • Reviews on the fRG approach in gauge theories, QCD & gravity

    •   Pawlowski Aspects of the FRG Annals Phys.322:2831-2915,2007
      Gies Introduction to the FRG and applications to gauge theories Lect.Notes Phys. 852 (2012) 287-348
      Braun Fermion Interactions and Universal Behavior in Strongly Interacting Theories J.Phys. G39 (2012) 033001
      Reuter, Saueressig Quantum Einstein Gravity New J.Phys. 14 (2012) 055022
      Litim Renormalisation group and the Planck scale Phil.Trans.Roy.Soc.Lond. A369 (2011) 2759-2778
      Eichhorn Status of the asymptotic safety paradigm for quantum gravity and matter Class.Quant.Grav. 35 (2018) no.4, 044001
      Niedermaier, Reuter The Asymptotic Safety Scenario in Quantum Gravity Living review
      Reichert Functional Renormalisation Group and Asymptotically Safe Quantum Gravity 15th Modave Summer School in Mathematical Physics
      Bonanno, Eichhorn, Gies, Pawlowski, Percacci, Reuter, Saueressi, Vacca Critical reflections on asymptotically safe gravity Front.in Phys. 8 (2020) 269
      Pawlowski, Reichert Quantum gravity: a fluctuating point of view Front.in Phys. 8 (2021) 527
      Pawlowski, Reichert Quantum Gravity from dynamical metric fluctuations https://arxiv.org/abs/2309.10785


  • Reviews on DSEs in QCD

    • Alkofer, von Smekal The Infrared Behavior of QCD Green's Functions Phys.Rept.353:281,2001
      Fischer Infrared Properties of QCD from Dyson-Schwinger equations J.Phys.G32:R253-R291,2006
      Fischer QCD at finite temperature and chemical potential from Dyson-Schwinger equations Prog.Part.Nucl.Phys. 105 (2019) 1-60

    Literature, basics


  • Textbooks on the renormalisation group and critical phenomena

    • Amit Field Theory, the Renormalization Group, and Critical Phenomena World Scientific
      Binney, Dowrick, Fisher, Newman The Theory of Critical Phenomena, an Introduction to the Renormalization Group Clarendon Press, Oxford
      Cardy Scaling and Renormalization in Statistical Physics Cambridge University Press
      Collins Renormalization Springer
      Parisi Statistical Field Theory Addison-Wesley
      Zinn-Justin Quantum Field Theory and Critical Phenomena Claredon Press, Oxford