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I am looking for textbooks, lecture notes, lecture videos on rigorous introductions to condensed matter physics. I'd prefer to not be referred to monographs for an introduction as they tend to be quite dense in my experience. I would however, be welcome to try any that are actually written from a pedagogical perspectove. What I am looking for are resources with a level of rigor equivalent to Thirring's Quantum Mathematical Physics, but I could settle for books like Talagrand's What Is A Quantum Field Theory? which is quite rigorous to some level and sympathetic to concerns for rigor in any non-rigorous essential methods/tools used by physicists.

As for my background, I'm a master's student in physics and I have a fair idea about the physics lingo on these subjects and have taken courses on them. I also have background on axiomatic quantum theory, group theory and differential geometry. However, I'm looking to start afresh with more precise terminology and a well-organised Definition-Theorem-Proof kind of approach. I prefer resources that are comprehensive (covering roughly the topics in Girvin and Yang's Modern Condensed Matter Physics) and pedagogically oriented with sufficient attention to the applications (in at least, the form of problems) as opposed to dense travesties that only focus on the mathematics itself. To cite an example for what I mean by this, I would, for learning mathematical analysis choose a Zorich over a Rudin anyday.

PS: I hope that paints a clear picture of what I need and hopefully I can be directed to such resources. I have carefully looked at similar questions to mine but haven't found any material that I would consider introductory, be it in the comments or the answers to those questions.

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    Are you aware of the MIT open courses in physics? https://ocw.mit.edu/search/?d=Physics&s=department_course_numbers.sort_coursenum . there are graduate courses also – anna v Sep 26 '22 at 18:11
  • @annav , I am aware of MIT OCW. However these typically don't cater to the style I mentioned. Most of the rigorous content are offered by the math department and they do not have the attention to physics and comprehensiveness I am looking for. If you are aware of any that I may have overlooked, feel free to recommend. – Song of Physics Sep 26 '22 at 18:31
  • The Stability of Matter in Quantum Mechanics by E. Lieb and R. Seiringer might be of interest to you, although I don't know if this is what you mean with 'condensed matter' - a huge field. – Tobias Fünke Sep 26 '22 at 18:40
  • @JasonFunderberker this book does fit the style I require (and I will take a look), however I feel that it may be too restrictive. I would prefer something more comprehensive in terms of content such as Girvin and Yang's Modern Condensed Matter Physics, but with more attention to rigour of course. A collection of smaller resources to learn this content would also be fine. I understand that I am being extremely picky, but I hope I can find what I'm looking for. – Song of Physics Sep 26 '22 at 19:01
  • Regarding general many-body notes (second quantization, Bogoliubov theory etc.) I'd also recommend J.P. Solovej's lecture notes: Many Body Quantum Mechanics, which are available online or the lecture notes 'Mathematical Quantum Mechanics II' by Phan Thành Nam, which should be available, too. However, I don't know any book that fits your requirements regarding general condensed matter physics. I'd be interest too :) – Tobias Fünke Sep 26 '22 at 19:54
  • @JasonFunderberker thank you. These notes are good places to start imo. A few more notes like these for a more complete reading is all I need! It would indeed be great if all this could be packed into a single book though :) – Song of Physics Sep 26 '22 at 20:17
  • How about "Methods of Quantum Field Theory in Statistical Physics" by Abrikosov et al. – hft Sep 26 '22 at 21:01
  • @hft I've come across the book before but it sadly doesn't fit my needs. I do have a far more rigorous and pedagogical book on "Statistical Mechanics of Lattice Systems" by Friedli and Velenik which covers some things that I'm looking for of course. – Song of Physics Sep 27 '22 at 03:28
  • @Anyon I guess you've confused the two questions. – Tobias Fünke Sep 27 '22 at 09:39
  • @JasonFunderberker Yes, my bad for having too many open tabs... The related question I meant to link is Mathematical rigorous introduction to solid state physics – Anyon Sep 27 '22 at 13:15
  • @Anyon I have checked this link before and I have made a short list from some of the answers. Most of the references are focused on topological matter, hall effect and renormalization however. While the electronic structure and crystallography references are quite nice, the totality is still lacking in either the comprehensive coverage I'm looking for or the level of rigour. – Song of Physics Sep 28 '22 at 03:32

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