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.).
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.- 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.
- 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
- The perfect book for an introduction at an undergraduate level: Introduction to electrodynamics (4. ed), Griffiths
- Very famous, but quite old, and the problems are notoriously very difficult: Classical Electrodynamics, Jackson
- Collaborative solutions to the Problems in the Jackson: Physics is Beautiful
- My favourite, very complete and with lots of exercises: Modern Electrodynamics, Zangwill
Quantum Mechanics
- 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).
- Perfect for a first course on QM at an undergraduate level: Introduction to Quantum Mechanics, Griffiths
- Notes of Noah Miller (Harvard) on the use of representation theory in QM, very well written (PDF): Representation Theory and Quantum Mechanics
- Very interesting book on the use of symmetries in QM by Zwicky (PDF): Symmetries of Quantum Mechanics
- Good book on the use of group theory in QM: Quantum Theory, Groups and Representations, Woit
- Representation theory in QM (PDF): Understanding Quantum Mechanical Systems with Spherical Symmetry via Representations of Lie Groups, Greif
- Before the exam: Problems and Solutions in Quantum Mechanics, Tamvakis
Particle and Nuclear Physics
- Good introductory book on the subject: The Basis of Nuclear and Particle Physics, by Belyaev and Ross.
- Summary of the experimental concepts: Techniques for Nuclear and Particle Physics Experiments, W.R. Leo.
- Another good textbook on the subject: Particle Physics (3rd. ed.), by B.R. Martin.
- To practice before the exam: 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
- 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 techiques. The best introduction to renormalization I've seen.
- Tong, Gauge Theory. Additional, but useful details.
- Nair, Quantum Field Theory, A Modern Perspective. Includes strongly coupled theories.
Topological Quantum Field Theory
- TBC
General Relativity
- Caroll, Spacetime and Geometry. An excellent introduction to GR.
- Aretakis, Lecture Notes on General Relativity, Columbia University.
- Harvey Reall, Part III General Relativity. Lecture notes used at Cambridge.
- Compère & Fiorucci's Advanced Lectures on General Relativity deal with topics that are not usually mentionned elsewhere.
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 of Cambridge (Dorey)
- Fuchs, Schweigert, Symmetries, Lie Algebras and Representations: a Graduate course for Physicists. Very good.
Generalized & Non-Invertible Symmetries
- TBC
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 lookg at Prof. Tong's notes on Gauge Theory, especially when looking at (S)QCD.
String Theory
- Tong, String Theory. Notes I used in Cambridge. Only deal with bosonic strings.
- Polchinsky, String Theory, Vol.1 & Vol.2. The reference textbook.
- I really liked Becker-Becker-Schwarz & Timo Weigand's notes, especially for superstrings and M-theory.
- The amazing String Theory Wiki contains plently reviews, resources, conferences, etc. 200% worth checking!!!
Topological String Theory
- TBC
Solitons, Instantons, Twistor Theory
- Manton, Topological Solitons
- Dunajski, Solitons, Instantons and Twistors
- Adamo, Lectures on Twistor Theory
Gauge/gravity duality, AdS/CFT
- TBC
Flat space holography
- TBC
Integrability
- 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.
- Ressources of the Archimedeans, the Cambridge University Mathematical Society.
- Archives (lectures notes + example sheets) 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.