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The Attempted Proof of the Spin-Statistics Theorem
by Frederik Jozel Belinfante

Frederik Jozel Belinfante was born in the Netherland in the city known as The Hague. His intellectual ability was recognized early and he acquired first class training in physics. He received his Ph.D. in physics at the University of Leiden in 1939 under the direction of H.A. Kramers. This association with Kramers was critical in the direction of his work. Kramers had just postulated that the Lagrangian for any particle should be invariant under the transformation of charge. This turned out not to be valid but it was the first step toward what is known as the TCP Theorem. The TCP refers to transformation of particle Lagrangians by Time inversion, Charge inversion and Parity inversion.

Belifante based his proof of the Spin-Statistics Theorem on charge conjugation. Unfortunate he chose to create mathematical entities which he called undors. An undor of the first rank is a four component Dirac spinor the first two components of which are covariant and the last two components of which are countervariant. An undor of the second rank has sixteen components. Obviously the calculus of undors is exceedingly cumbersome and obscure.

To make matters even more difficult Belifante filled his writing with terms he coined such as neutrinors, neutrettos and hystatons. None of these terms were accepted elsewhere. Belifante did not hesitate to use his coined terms. The title of his article was "The Undor Equation of the Meson Field." However, perhaps as a result of Belifante's efforts. the term nucleon emerged as a useful term for neutrons and protons.

Belifante's work was notable primarily as the first step in the direction of proving the Spin-Statistics Theorem based on the TCP Theorem, which is now accepted as the rigorous approach.


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

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