Wikipedia's article on the spin-statistics theorem sums it up thusly:
In quantum mechanics, the spin-statistics theorem relates the spin of a particle to the particle statistics it obeys. The spin of a particle is its intrinsic angular momentum (that is, the contribution to the total angular momentum which is not due to the orbital motion of the particle). All particles have either integer spin or half-integer spin (in units of the reduced Planck constant ħ).
The theorem states that:
- the wave function of a system of identical integer-spin particles has the same value when the positions of any two particles are swapped. Particles with wavefunctions symmetric under exchange are called bosons;
- the wave function of a system of identical half-integer spin particles changes sign when two particles are swapped. Particles with wavefunctions anti-symmetric under exchange are called fermions.
In other words, the spin-statistics theorem states that integer spin particles are bosons, while half-integer spin particles are fermions.
Question. What would you recommend as the best means to understanding the proof of the spin statistics theorem? To put it another way: if you took (for instance) the proof-sketch for the spin-statistics theorem given later in that same Wikipedia page, and wanted to add enough material to it to create a textbook whose entire purpose was to take someone from a third- or fourth-year undergrad level of physics up to understanding the spin-statistics theorem inside-out, what references would you use to flesh out the material of that book?
Context. I'm a researcher in quantum computation, coming from the computer science end of things: I have a very solid grasp on the basic mathematical framework of non-relativistic QM, and some special relativity, if not all applicable techniques. I have very basic familiarity with fermionic and bosonic operator algebras, as algebras generated by creation/annihilation operators satisfying certain axioms, though I have not had occasion to use them much myself.
I take for granted that understanding the proof of the spin-statistics theorem will involve learning a non-trivial amount of physics (and also likely mathematical) background.
Any recommendations?
Edited to add: If it is sufficient to learn quantum field theory, please recommend a suitable text as an answer. For instance, if you know of a good book on QFT that does not assume much of a background in particular topics such as E&M, and which definitely covers all of the concepts pertinent to the proof-sketch given on the Wikipedia page, and/or itself has a good self-contained proof of the spin-statistics theorem — in short, a book which can take me from Schrödinger and Einstein all the way to the spin-statistics theorem — then please recommend the book in question as an answer.
Best Answer
I wrote the Wikipedia page in question, so I feel bad. I thought it was clear.
There is a recent textbook by Banks which covers the spin/statistics theorem pretty good. I hope it is ok. The main difficulty is that there is no quantum field theory book that covers analytic continuation to Euclidean space, and this is the essential thing.
This is worked out by each person on their own, as far as I know. The problem is that it is very easy to say "plug in i times t everywhere you see t" and get 90% of everything right, without understanding anything. Streater and Whitman do it, that's most of their book, but they are too formal to be comprehensible. Schwinger is too long ago (and ideosyncratic). Perhaps the statistical section of Feynman and Hibbs (Path integrals), where they actually rederive the path integral in imaginary time, will allow you to extrapolate to the general bosonic fields.
The Fermionic case requires the Euclidean continuation of Majorana spinors, and this was in the literature more recently: http://arxiv.org/abs/hep-th/9608174. This stuff is covered in none of the textbooks, and unfortunately I can't recommend any of them with a good conscience.
Later Edit: If you don't want to go to Euclidean space, you should avoid anything past Feynman/Schwinger. The best path then is possibly to work through Pauli's argument:W. Pauli, The Connection Between Spin and Statistics, Phys. Rev. 58, 716- 722(1940).