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Is this proof of spin-statistics theorem correct?

http://bolvan.ph.utexas.edu/~vadim/classes/2008f.homeworks/spinstat.pdf

This proof is probably a simplified version of Weinberg's proof. What is the difference?

What is the physical meaning of $J^{+}$ and $J^{-}$ non-hermitian operators?

I'm especially interested in the beginnig of proof of second lemma. How to get this: \begin{eqnarray} F_{AB}(-p^{\mu}) = F_{AB}(p^{\mu})\times (-1)^{2j_{A}^{+}} (-1)^{2j_{B}^{+}} \\ \nonumber H_{AB}(-p^{\mu}) = H_{AB}(p^{\mu})\times (-1)^{2j_{A}^{+}} (-1)^{2j_{B}^{+}} \end{eqnarray}

Also why under CPT field transform as \begin{eqnarray} \phi_{A}(x)\rightarrow \phi_{A}^{\dagger}(-x) \times (-1)^{2J_{A}^{-}} \\ \nonumber \phi_{A}^{\dagger}(x) \rightarrow \phi_{A}(-x) \times (-1)^{2J_{A}^{+}} \end{eqnarray} conjugation is from charge reversal, - from space inversion and time reversal. What about $(-1)^{2J_{A}^{-}}$?

Where can I find similar proofs?

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closed as too localized by joshphysics, Waffle's Crazy Peanut, user1504, Brandon Enright, David Z Jun 3 '13 at 18:51

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"Is this proof correct" isn't a conceptual question. Do you have a question about a particular step in the paper? –  Brandon Enright May 28 '13 at 23:59