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I'd like to get acquainted with the basics of mathematical rigorous second quantization, so I'm looking for an adequate reference on this subject. I've a background in quantum mechanics, but I don't know much on quantum field thery (I don't know to what extent it is necessary to understand second quantization). The point is: my research area is rigorous statistical mechanics, so I don't intend to become an expert on the subject, but I need to understand at least the basics. The only reference I know is The Method of second quantization by F. Berezin. So far, I've just skimmed the book and it seems incredibly well-written, but it is obviously an old book and I feel it is not very modern concerning its mathematics: I'd be happier to find a more technical exposition, using modern functional analysis. However, I don't know if this reasoning is just a reflection of the fact that I know hardly nothing on the subject. So I ask: is Berezin's book the best place to start? Are there other (more technical, maybe) references on the subject? Thanks in advance!

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§X.7 of Reed & Simon's Methods of Modern Mathematical Physics v.2 (Academic Press, 1975) starts out with the epigraph First quantization is a mystery, but second quantization is a functor. E. Nelson. It's pretty rigorous.

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  • $\begingroup$ Great! I love these collection and I pretty much like everything Reed and Simon write. This sounds perfect! $\endgroup$ – IamWill Aug 14 at 15:24
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One book which may be useful to you is by Edson De Faria's: Mathematical aspects of QFT.

The tract has been written by someone who definitely has a strong background in physics but is nevertheless a mathematician (former student of the famous geometer Dennis Purnell Sullivan). As you may know, there are different ways to introduce QFT, one being via Lagrangian densities, another via the Fock space (and there are others, for instance the categorical approach). This text does not cover all of them, but it is definitely something a math-oriented fellow can enjoy

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    $\begingroup$ Great answer! Thank you so much! I'll definitely read Edson's book. Btw, what's your opinion on Dimock's book "Quantum Mechanics and Quantum Field Theory"? It seems very good too. $\endgroup$ – IamWill Aug 14 at 15:23
  • $\begingroup$ simple answer: I have no opinion, because I have not read it ! But now I am going to check it out... as an aside, I know what I would LOVE to see in a book on QFT: some articulated discussion on how the different presentations are related to one another. Never seen anything like it.. $\endgroup$ – Mirco A. Mannucci Aug 14 at 15:25
  • $\begingroup$ PS I knew Edson quite well: we were writing our dissertations in the same crammed room some centuries ago. If you read the book and wish to reach out to him, do it: Edson is a very nice fellow, $\endgroup$ – Mirco A. Mannucci Aug 14 at 15:28
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    $\begingroup$ the world is small indeed.... if you catch up with Edson send him the best from the crazy italian :) $\endgroup$ – Mirco A. Mannucci Aug 14 at 15:36
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    $\begingroup$ Nice! I'll keep that in mind! $\endgroup$ – IamWill Aug 14 at 15:41

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