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
- 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.
- Check out the videos of 3Blue1Brown, Mathemaniac, Mathologer, Michael Penn, Mu Prime Maths, Numberphile, and blackpenredpen on YouTube (integration, differential equations, etc.).
Undergraduate physics
Statistical Physics
- I found the first chapters quite clear: Statistical Physics (2 ed), Huang.
- These were the lecture notes of the course I took, lectured by Prof. Manfred Sigrist.
- 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
- The perfect introduction at an undergraduate level: Introduction to electrodynamics, Griffiths.
- My personal favourite, very complete and with lots of exercises: Modern Electrodynamics, Zangwill.
Quantum Mechanics
- On the path integral approach to Quantum Mechanics: Quantum Mechanics and Path Integrals, Feynman. For a first contact with QM, I would rather recommend the Hamiltonian approach: Introduction to Quantum Mechanics, Griffiths.
- Notes of Noah Miller on Representation Theory and Quantum Mechanics, very well written.
- Good book on the use of group theory in QM: Quantum Theory, Groups and Representations, Woit.
- Representation theory in QM: Understanding Quantum Mechanical Systems with Spherical Symmetry via Representations of Lie Groups, Greif.
- To practice before the exam: Problems and Solutions in Quantum Mechanics, Tamvakis.
Particle and Nuclear Physics
- The classic introductory textbooks on the subject are The Basis of Nuclear and Particle Physics by Belyaev and Ross, Techniques for Nuclear and Particle Physics Experiments by W.R. Leo, and Particle Physics (3rd. ed.) by B.R. Martin.
- To practice: Problems and Solutions of Atomic, Nuclear and Particle Physics, by Yung-Kuo Lim.
Graduate physics
Quantum Field Theory
- My favorite: QFT and the Standard Model, by Matt Schwartz. Easier to read than Weinberg.
- Tong's notes on QFT, used for the first part of the course in Cambridge. Only canonical quantization.
- The notes of Prof. Beneke for the course I took at TUM. Based on Weinberg, with a focus on path integral techniques. The best introduction to renormalization I've seen. See also the typed script of Prof. Weiler, which follows closely the notes of Beneke. The exercises are also very good.
- Tong, Gauge Theory. Additional, but useful details. Very complete set of notes.
- Nair, Quantum Field Theory, A Modern Perspective. Also discusses strongly coupled theories.
- See the lecture notes of Prof. Tancredi (TUM) on Advanced QFT.
General Relativity
- Caroll, Spacetime and Geometry. Easy to read, good introduction.
- Harvey Reall, Part III General Relativity. Lecture notes used when in Cambridge.
- And the follow-up notes on black holes by Townsend and Reall. Both excellent.
- 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
- Hall, Lie Groups, Lie Algebras and Representations, the reference textbook.
- Humphreys, Introduction to Lie Algebras and Representation Theory slightly easier to read.
- Ashok Das, Lie Groups and Lie Algebras for Physicists, lacking some maths but fairly intuitive.
- Ian Lim, Symmetries, Field and Particles, based on the course I had in Cambridge (Prof. Dorey).
- Fuchs, Schweigert, Symmetries, Lie Algebras and Representations: a Graduate course for Physicists.
Supersymmetry
- The lecture notes of Prof. Tong, on SUSY & Duality. Prof. Tong was my lecturer in Cambridge.
- 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.
- It can also be worth looking at Prof. Tong's notes on Gauge Theory.
- The lecture notes of Bertolini are a must!
String Theory
- Tong, String Theory. Notes I used in Cambridge. Great introduction to bosonic strings.
- My favourite, Basic Concepts of String Theory by Blumenhagen, Lüst and Theisen.
- I really liked Becker-Becker-Schwarz, easy to read.
- The amazing String Theory Wiki contains plently reviews, resources, conferences, etc.
Solitons, Instantons, Twistor Theory
- Adamo, Lectures on Twistor Theory. A very good place to start with twistors.
- TBC.
Research-specific, reviews
Flat-space holography
- TBC
String amplitudes
- TBC
Non-Lorentzian string theory
- TBC
General websites
- Archives of the Institute for Theoretical Physics at ETH Zürich: ITP Lecture Archive.
- Archives of the lectures at MIT: MIT OpenCourseware. Quite time-consuming though.
- Teaching page of Prof. Tong at the University of Cambridge: David Tong, aka the god of teaching.
- Resources of the Archimedeans, the Cambridge University Mathematical Society.
- Archives of the Part III in Applied Mathematics at the University of Cambridge
- Archives of the Examples for the Mathematical Tripos (undergraduate curriculum) at Cambridge.
- Online courses at the Perimeter Institute
- Excellent lectures on the Geometrical anatomy of Theoretical Physics by Prof. Schüller
- The great String Theory Wiki, with dozens of resources, reviews, etc.
