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Introduction to Renormalization

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Introduction to Renormalization with Applications in Condensed-Matter and High-Energy Physics Institute for Theoretical Physics, University of Cologne Lecture course, winter term 2017/2018. Michael M. Scherer January 26, 2021. Contents Contents 1. 1 Introduction 5. Aspects of the Renormalization group . . . . . . . . . . . . . . . . . . . . . . . 6. Phase transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Critical phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Perturbative quantum field theory . . . . . . . . . . . . . . . . . . . . . . . . 9. Renormalization - group based definition of QFTs . . . . . . . . . . . . . . . . 10. QFTs in the high-energy limit . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. 2 Phase transitions and critical phenomena 13.

Renormalization-group methods are relevant to a large diversity of elds)many (apparently) di erent implementations)sometimes hard to access!Functional RG provides uni ed formulation. 1.2 Phase transitions • Sketchy phase diagram of water: theory space S! + h T Tc m ! 0 m = 0 m > 0 m < 0 FM PM temperature r

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