Mathematical rigorous introduction to solid state physics

Question

I am looking for a good mathematical rigorous introduction to solid state physics. The style and level for this solid state physics book should be comparable to Abraham Marsdens Foundations of mechanics or Arnols mechanics book for classical mechanics or to Thirrings Physics course for quantum mechanics.

Any recommendations?

Edit: As a reaction to Peter Shor's comment, I try to narrow the scope of the question a bit and give some more specific subareas of solid state physics I am in particular interested in:

• semiconductors and applications
• the quantum hall effect
• superconductivity

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Comments

Solid-state physics is an enormous field; do you have any specific subareas of solid-state physics that you'd like a mathematically rigorous introduction to?

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As a non-mathematician I've never gotten around to reading this, but it might be of interest since you mentioned QHE -- arxiv.org/abs/cond-mat/9411052

Answer 1

The following books discuss rigorous methods in solid state physics:

• "Renormalization group" by G. Benfatto and G. Gallavotti, see this link.
• "Renormalization: an introduction" by M. Salmhofer, see this link.
• "Fermionic functional integrals and the renormalization group", J. Feldman, H. Knorrer and E. Trubowitz, see this link.
• "Non-perturbative renormalization" by V. Mastropietro, see this link.

See also the course by Rivasseau given at the CIME school in Cetraro, September 2010.

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Answer 2

You can wonder about the stability of matter in quantum mechanics or get caught by disorder to learn the rigorous aspects of localization in disordered systems.

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Answer 3

The problem with this kind of books is that there is no special mathematics in solid state physics. There are books with titles like "Quantum Field Theory in Solid State Physics" or similar: modern methods in solid state originate from QFT, quantum chemistry and alike. Thus, rigorous introduction may be found there and not in solid state itself.

If you could specify particular topic, probably it would be possible answer your question.

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Comments

Agreed. Also, if @student is taking his first course in SSP, he should, perhaps, pick a standard text such as Ashcroft/Kittel, for it is hard to say what mathematics are more important. In quantum many-body theory your main tool may be QFT, linear algebra, group theory or category theory depending on the field.

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@JuanBermejoVega No I am not taking my first course in SSP, however I am by far not an expert in this field. Coming from mathematical physics I just want to have a second introduction which is more rigorous (both mathematical and conceptual) than the standard ones.

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Then, if the answers above don't suffice, you could maybe specify your favourite topics.

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