Notes & Resources

A compilation of lecture notes, moocs and webpages which I have found being worth browsing along the way. Unless stated otherwise, all resources are available in English. This page is under construction, so it might be a bit messy in some places :) Some links might also be broken; in that case please reach out and I'll try to fix it.

Undergraduate

Mathematics

  1. Hundreds of exercises (in French) to practice differential calculus and analysis: Analyse - recueil d’exercices et aide mémoire. (Jacques Douchet) Vol.1 and Vol.2.
  2. Check out the videos of 3Blue1Brown, Mathemaniac, Mathologer, Michael Penn, Mu Prime Maths, Numberphile, and blackpenredpen on YouTube (integration, differential equations, etc.).

Physics

Statistical Physics

The following is based on a Master-level course I took while at ETHZ (3rd year of my BSc. in Physics), having already had an education in Thermodynamics.
  1. I found the first chapters quite clear: Statistical Physics (2 ed), Huang
  2. These were the lecture notes of the course I took, lectured by Prof. Manfred Sigrist.
  3. As always, I can’t but recommend checking out Prof. Tong’s lecture notes (it might be worth checking out the notes on Statistical Field theory as well, but this is definitely graduate level).

Classical Electrodynamics

  1. The perfect introduction at an undergraduate level: Introduction to electrodynamics (4. ed), Griffiths
  2. My favourite, very complete and with lots of exercises: Modern Electrodynamics, Zangwill

Quantum Mechanics

  1. On the path integral approach to Quantum Mechanics, by the great Feynman: Quantum Mechanics and Path Integrals, Feynman. For a first contact with QM, I would rather recommend the Hamiltonian approach (eg. Griffiths).
  2. Perfect for a first course on QM at an undergraduate level: Introduction to Quantum Mechanics, Griffiths
  3. Notes of Noah Miller on Representation Theory and Quantum Mechanics, very well written.
  4. Very interesting book on the use of symmetries in QM by Zwicky: Symmetries of Quantum Mechanics
  5. Good book on the use of group theory in QM: Quantum Theory, Groups and Representations, Woit
  6. Representation theory in QM Understanding Quantum Mechanical Systems with Spherical Symmetry via Representations of Lie Groups, Greif
  7. Before the exam: Problems and Solutions in Quantum Mechanics, Tamvakis

Particle and Nuclear Physics

  1. Good introductory book on the subject: The Basis of Nuclear and Particle Physics, by Belyaev and Ross.
  2. Summary of the experimental concepts: Techniques for Nuclear and Particle Physics Experiments, W.R. Leo.
  3. Another good textbook on the subject: Particle Physics (3rd. ed.), by B.R. Martin.
  4. To practice: Problems and Solutions of Atomic, Nuclear and Particle Physics, by Yung-Kuo Lim.

Graduate

The following are from the courses I took or am currently taking in Cambridge/Munich. I have also included some that I've browsed for my independent study. As you might notice, my interests are heavily HEP & GR-focused!

Theoretical Physics

Quantum Field Theory

  1. My favorite: QFT and the Standard Model, by Matt Schwartz. Easier to read than Weinberg.
  2. Tong's notes on QFT, used for the first part of the course in Cambridge. Only canonical quantization.
  3. The notes of Prof. Beneke for the course I took at TUM. Based on Weinberg, with a focus on path integral techiques. The best introduction to renormalization I've seen.
  4. Tong, Gauge Theory. Additional, but useful details.
  5. Nair, Quantum Field Theory, A Modern Perspective. Includes strongly coupled theories.

Topological Quantum Field Theory

  1. TBC

General Relativity

  1. Caroll, Spacetime and Geometry. Easy to read, good introduction.
  2. Harvey Reall, Part III General Relativity. Lecture notes used when in Cambridge.
  3. And the follow-up notes on black holes by Townsend and Reall. Both excellent.
  4. Compère & Fiorucci's Advanced Lectures on General Relativity deal with topics that are not usually mentionned elsewhere, while MTW gives the good old introduction to GR.

Symmetries in Physics, Lie Groups & Representation Theory

  1. Hall, Lie Groups, Lie Algebras and Representations, the reference textbook.
  2. Humphreys, Introduction to Lie Algebras and Representation Theory slightly easier to read.
  3. Ashok Das, Lie Groups and Lie Algebras for Physicists, lacking some maths but fairly intuitive
  4. Ian Lim, Symmetries, Field and Particles, based on the course of Cambridge (Dorey)
  5. Fuchs, Schweigert, Symmetries, Lie Algebras and Representations: a Graduate course for Physicists. Very good.

Generalized & Non-Invertible Symmetries

  1. TBC

Supersymmetry

  1. The lecture notes of Prof. Tong, on SUSY & Duality. Prof. Tong was my lecturer in Cambridge.
  2. Muller-Kirsten, Introduction to Supersymmetry. I used this book a few times to check calculations, most of them are done in great detail, where other authors would just omit the steps.
  3. It can also be worth lookg at Prof. Tong's notes on Gauge Theory, especially when looking at (S)QCD.

String Theory

  1. Tong, String Theory. Notes I used in Cambridge. Great introduction to bosonic strings.
  2. My favourite, Basic Concepts of String Theory by Blumenhagen, Lüst and Theisen.
  3. I really liked Becker-Becker-Schwarz & Timo Weigand's notes, especially for superstrings and M-theory.
  4. The amazing String Theory Wiki contains plently reviews, resources, conferences, etc.
  5. Bilal has excellent lecture notes on anomalies, with a chapter dedicated to their role in string theory.

Solitons, Instantons, Twistor Theory

  1. Adamo, Lectures on Twistor Theory. A very good place to start with twistors.
  2. I mainly used Vandoren Lectures on Instantons and Tong's TASI Lectures on Solitons.
  3. CERN's lecture notes on Instantons in Gauge theories, or this paper by Dorey et al. also provided useful additional details, for instance on the ADHM construction.

General websites

  1. Archives of the Institute for Theoretical Physics at ETH Zürich: ITP Lecture Archive.
  2. Archives of the lectures at MIT: MIT OpenCourseware. Quite time-consuming though.
  3. Teaching page of Prof. Tong at the University of Cambridge: David Tong, aka the god of teaching.
  4. Ressources of the Archimedeans, the Cambridge University Mathematical Society.
  5. Archives (lectures notes + example sheets) of the Part III in Applied Mathematics at the University of Cambridge
  6. Archives of the Examples for the Mathematical Tripos (undergraduate curriculum) at Cambridge.
  7. Online courses at the Perimeter Institute
  8. Excellent lectures on the Geometrical anatomy of Theoretical Physics by Prof. Schüller
  9. The great String Theory Wiki, with dozens of resources, reviews, etc.