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The Second Attempted Proof of the Spin-Statistics Theorem
by Wolfgang Pauli (1940)

Wolflgang Pauli

After his attempted proof of the Spin-Statistics Theorem in 1936 was not accepted as definitive and after his criticism of proofs by others it was incumbent upon Pauli to produce a definitive such proof. He published his effort in 1940 while he was at the Institute for Advanced Study at Princeton, New Jersey. The title of his article, published in the Physical Review, was simply "The Connection between Spin and Statistics." The abstract read

For the relativistically invariant free-particle wave equations, we conclude: I) for the energy to be positive, Fermi-Dirac statisitcs must be used for particles of half-integral spin;II) for observables at spacelike separated points to commute, Bose-Einstein statistics must be used for particles of integral spin.

Following iin line with several attempted proofs in the late 1930's he presumed a particle could be represented by a type of spinor. These were divided into four class and labeled U(±1) for integral spin particles and U(plusmn;epsilon;) for half-integral spin particles. He found that integral spin fields can be quantized only using commutation (as opposed to anti-commutation) relations. Duck and Subarshan note

For half-integral spins, Pauli finds no such general restriction. Both commutation and anticommutation are permitted a priori. He then must have recourse to the requirement of postive energies to restrict the possibilities to anticommutation relations.

After World War II the physics profession came to accept a different approach not involving spinors to proving the Spin-Statistics Theorem. Pauli went on to other endeavors outside of physics. Pauli started seeing Carl Jung about his problem with depression and ended up colaborating with Jung in works on creativity. He died in 1958 at the relatively young age of 58.

Wolfgang Pauli
(To be continued.)


Ian Duck and E.C.G. Sudarshan, Pauli and the Spin-Statistics Theorem,, World Scientific, Singapore, 1997.

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