Transcription of Introduction to Renormalization
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Introduction to Renormalization
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 .. 14. Symmetries of the Ising model .. 15. XY model and Heisenberg model .. 15. Universality and critical exponents .. 16. Scaling hypothesis for the free energy .. 17. Derivation of power laws from scaling hypothesis .. 18. First attempt to calculate critical exponents .. 19. Correlations and hyperscaling .. 20. Ginzburg-Landau-Wilson theory .. 22. Functional integral representation of the partition function.
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.
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