Roadmap to self-studying relativity and quantum field theory

Hello! I'm interested in rigorously learning general relativity and quantum field theory by myself. I'm aware this will be no easy task! I have a MEng engineering degree so am lacking on the 'pure' physics side of things but I feel I have enough foundations for this not to be impossible given enough dedication.

Things I have a decent understanding of from prior study:

• Classical mechanics and dynamics (Newtonian)
• Lagrangian mechanics
• Basic quantum mechanics (e.g. solving the Schrodinger equation in the hydrogen atom and quantum harmonic oscillator)
• Quantum chemistry (molecular orbital theory)
• Linear algebra (including matrices as linear transformations)
• Partial differential equations (and ODEs, multivariable/vector calculus)
• Calculus of variations
• Complex analysis

Things I have no understanding of at all:

• Tensors and tensor calculus
• Differential geometry
• Special relativity (even the 'basic' explanations boggle my mind!)
• Group theory (I have come across crystallographic point groups in chemistry but only the bare basics).

What resources (books, videos, notes) should I use, and in which order? I watched through this video series on the maths of GR by ScienceClic and it was great but I want to go a bit deeper and build up an understanding of the various tools from a pure maths perspective.

Thanks for any advice!

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I've asked ChatGPT for some resources and it gave me a few things to check out. Would you recommend any of these?

• “A Student's Guide to Vectors and Tensors” by Daniel Fleisch
• “Lecture Notes on General Relativity” by Sean Carroll
• “Group Theory in a Nutshell for Physicists” by A. Zee
• “Introduction to Special Relativity” by James H. Smith
• “Spacetime and Geometry” by Sean Carroll
• “Quantum Field Theory for the Gifted Amateur” by Lancaster and Blundell