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Non-perturbative aspects of gauge theories

Jan Martin Pawlowski, Nicolas Wink, winter term 2020/2021
Tutor: Nicolas Wink

Lectures: Monday & Wednesday 11:15-13:00, gHS Pw 12 [LSF]

Tutorial: Monday 16:15-18:00

Current Modus: Lectures online with streaming, Tutorial online


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


Content of lecture series

The lecture course provides an introduction to the strongly-correlated physics of QCD and Quantum Gravity. The related physics problems are treated within the Functional Renormalisation Group (FRG), and a survey of alternative approaches is provided.

    Outline

  • The Functional RG

    • Derivation

    • Truncation schemes, optimisation & numerics

    • Fixed points in the Functional RG

  • QCD

    • Introduction

    • Confinement & chiral symmetry breaking

    • Confinement-deconfinement phase transition at finite T

    • A glimpse at the QCD phase diagram

  • Quantum Gravity

    • Introduction

    • RG approach to quantum gravity

    • Fixed point structure of quantum gravity

    • Cosmological applications



Literature


  • Introductory reviews on 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 FRG in gauge theories, QCD & gravity

    • Litim, Pawlowski On gauge invariant Wilsonian flows Proceedings 'The ERG', Word Scientific '99
      Pawlowski On Wilsonian flows in gauge theories Habilitation thesis, Erlangen '02
      Pawlowski Aspects of the FRG Annals Phys.322:2831-2915,2007
      Schaefer, Wambach Renormalization Group Approach towards the QCD Phase Diagram Phys.Part.Nucl. 39 (2008) 1025-1032
      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
      von Smekal Universal Aspects of QCD-like Theories Nucl.Phys.Proc.Suppl. 228 (2012) 179-220
      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
      Dupuis, Canet, Eichhorn, Metzner, Pawlowski, Tissier, Wschebor The nonperturbative functional renormalization group and its applications https://arxiv.org/abs/2006.04853
      Pawlowski, Reichert Quantum gravity: a fluctuating point of view https://arxiv.org/abs/2007.10353


  • 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

    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


  • Quantum field theory, basics

    •   Haag Local Quantum Physics Springer, 1996
    Itzykson, Zuber Quantum Field Theory McGraw-Hill
      Peskin, Schroeder An Introduction to Quantum Field Theory Addison Wesley
      Siegel Fields hep-th/9912205
      Weinberg The Quantum Theory of Fields, Vol. 1-2 Cambridge University Press


  • Quantum field theory, applications

    • Kugo Eichtheorie Springer, 1997
      Miransky Dynamical Symmetry Breaking in Quantum Field Theories World Scientific, 1993
      Muta Foundations of Quantum Chromodynamics World Scientific, 1987
      Pokorski Gauge Field Theories Cambridge, 1987
      Wu-Ki Tung Group Theory in Physics World Scientific, 1985
      Zinn-Justin Quantum Field Theory and Critical Phenomena Oxford, 1993



  • General relativity

    •   Carroll Spacetime and Geometry Addison Wesley
    Göckeler & Schücker Differential Geometry, gauge theories, and gravity Cambridge University Press
      Misner, Torne, Wheeler Graviation Freeman