# Spin-Statistics Theorem (SST)

Please can you help me understand the Spin-Statistics Theorem (SST)? How can I prove it from a QFT point of view? How rigorous one can get? Pauli's proof is in the case of non-interacting fields, how it will be in the presence of interacting fields? The origins of the minus sign, when swapping the wave-function, it implies the CPT theorem in play (spinors, anti-articles)?

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Related: physics.stackexchange.com/q/13787/2451 and links therein. – Qmechanic Feb 3 '14 at 16:49

## 1 Answer

The classic place to start would be the book "PCT, Spin & Statistics, and All That", by R.F.Streater and A.S.Wightman. The spin statistics theorem can be proved as rigorously as you likely can want in the context of the Wightman axioms. The difficulty with this statement relative to your question is that we cannot prove that interacting fields satisfy the Wightman axioms.

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I am wary of recommending this book--- the proof is overly formal, and might not even be 100% correct. Their proof works in the Bosonic case, but the Fermionic case always left doubts, although the general idea is correct. The problem is that they do two rotations of 180 degrees, one in the x-t plane, the other in the y-z plane, to fix the spin-statistics, and I always just did one 180 degree rotation (see wikipedia and the talk page for SST). The second rotation can make polarizations flip, and I never checked Streater and Whitman's proof to see if it implies the relation for fermions. – Ron Maimon Apr 7 '12 at 5:05