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. Ising model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13. Remarks on solutions of the Ising model in d = 1 and d = 2.

1. Introduction In the following, I will rst discuss some of the aspects of the RG to give a rough overview. These di erent aspects will then be worked out in more detail during the lecture.