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I am looking for a book, or lecture notes or even courses available on YouTube where there is a good and detailed discussion on the mathematical aspects of Quantum Mechanics with infinite degrees of freedom. For what I have seen, this is usually described in terms of C* algebras for infinite degrees of freedom (like for example infinite tensor products of algebras of bounded operators on Hilbert spaces). Any idea?

Examples of what I am looking for (but I would like something more detailed, these are single chapters from books):

  1. "Symmetry Breaking", F. Strocchi, chapter "Mathematical description of infinitely extended quantum systems"
  2. "Deterministic Chaos in Infinite Quantum Systems", F. Benatti, chapter " Infinite quantum systems"
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    $\begingroup$ Is there a specific reason you're saying "quantum mechanics with infinite degrees of freedom" and not "quantum field theory"? $\endgroup$
    – ACuriousMind ♦
    Commented Sep 9, 2023 at 12:02
  • $\begingroup$ In case this is what you're looking for, Mathematical Foundations of Quantum Mechanics by Von Neumann. $\endgroup$
    – Bababeluma
    Commented Sep 9, 2023 at 12:14
  • $\begingroup$ @ACuriousMind Thank you for your question, I wanted to match the name of the mathematical approach that I have seen in books, expressed in terms of C* algebras. But I think you are right, the two should be the same. Just to clarify: I am not looking specifically at relativistic quantum field theory $\endgroup$
    – MBlrd
    Commented Sep 9, 2023 at 12:19
  • $\begingroup$ @Bababeluma thank you, I will have a look! $\endgroup$
    – MBlrd
    Commented Sep 9, 2023 at 12:22
  • $\begingroup$ But you are specifically looking at $C^\ast$-algebraic approaches? Because for instance Glimm and Jaffe's Quantum Physics is a mathematically rigorous look at quantum field theory but it uses the point of view of path integrals, not of operator algebras. I'm not sure if this within the scope of material you're asking for here or not from how the question is currently written $\endgroup$
    – ACuriousMind ♦
    Commented Sep 9, 2023 at 12:34

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