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Introduction to the functional renormalisation group and selected applications

Jan Martin Pawlowski, summer term 2025


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


Tutorial/Seminar: Monday 16:15-18:00, R 106 Pw 12 [HeiCO]



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 and their applications to emergent phenomena. Examples are the formation of bound states and condensation phenomena. The second half of the lecture course will include inverted class room elements and seminar talks.

    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 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

    Literature


  • 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