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I know that there are multiple generic QM book recommendation questions out there, however I am looking for something with specific parameters, hence why I am posting a new question for it.

The way I learned QM in University, it was from a very "physical" point of view - in particular - representation theory and its application to QM was nonexistent there.

So, I am kind of looking for a QM book that is somewhat similar to Wald's General Relativity book in scope and style. I want something that is written for physicists by physicists (Note: I know multiple QM books by mathematicians that mainly focus on making the functional-analytic foundations of QM rigorous. I don't care about that right now, I'm fine with heuristic/incorrect formulation of spectral theory and all that), but at the same time, emphasizes overall structure and general methodology, rather than being historical, being phenomenologically/"physically" motivated or focusing too much on "understanding through applications".

In particular, I am very much interested in

  • representation theory - as applied to QM; Many intro books skip this altogether, but then the QFT literature assumes I know it. Also there seems to be a big divide here between physicists' and mathematicians' exposition, which further makes this difficult for me to learn.

  • a very systematic and elaborate treatment on angular momentum and spin; This concept always seemed so ad-hoc, unmotivated (aside from "experiments, hurr durr"), and there always seemed to me that there is a great divide between non-relativistic QM notation & approach and a systematic application of spinors that is common in the QFT/GR literature. I'd like spinors and all that properly and detailed in my QM literature.

Any book recommendations along this line are much welcome.

Qmechanic
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Bence Racskó
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1 Answers1

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  1. Peter Woit - Quantum Theory, Groups, and Representations: An Introduction

This book is pretty much what you're looking for. It is a very representation-theory influenced presentation of QM, and the latter parts of the book delve into QFT. In my opinion, the book strikes a fine balance between standard QM textbooks and those with 'QM for mathematicians' in the title, which as you say seem to concern themselves with making rigorous the 'functional analytic foundations' of QM. You can access the book via Springerlink if you're enrolled in a university that has a subscription.

  1. Leslie Ballentine - Quantum Mechanics: A Modern Development

Chapter 3 is a masterpiece. Similar to Woit's book in the preference for rep.theory, but less mathematical.

  1. A. Zee - Group theory for physicists in a Nutshell

This is a book on groups, algebras, and their representations. However, Zee explores many of these concepts in the context of QM. There are very nice presentations of angular momentum and spin in Part IV of the book, titled 'Tensor, Covering, and Manifold'.

  1. P.A.M. Dirac - Principles of Quantum Mechanics

No explanation needed. While there certainly isn't a detailed treatment of spin groups etc., as far as I know this was one of the first (and still remains one of the few) physics books that properly built up QM from scratch. Most textbooks just throw at you the postulates of QM and then apply it left and right to example systems. But why are these postulates necessary? What are the features that we see in experiments that require a new, non-classical theory with a new mathematical formalism? How do these features determine the mathematical structure we choose? Dirac's book was one of the first, and still one of the very few, that attempts to answer such questions. Granted, some of the interpretational statements are dated, but still far better than the standard undergraduate textbooks we use in universities these days.

  1. There has been tremendous work done on the foundations of QM, and we have much better answers today to questions like 'what is state reduction aka wavefunction collapse?', 'what constitutes measurement?', 'if the measuring device and the system are quantum systems interacting, then why do we need the notion of collapse in the first place?', etc. I recommend reading the papers of Chris Fuchs, Asher Peres as an entree to this field.