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Quantum mechanics

Statistics given a spin

Nature volume 389, pages 127–129 (1997)Cite this article

Any student of quantum mechanics will know the Pauli exclusion principle — it is simply that no two identical fermions (particles with half-integer spin) can occupy the same quantum state. The exclusion principle is the reason why everyday matter doesn't collapse. It is usually just taken for granted, but as Feynman points out1, the absence of a simple explanation for this ‘principle’2,5 shows us that something deeper is at work. In non-relativistic quantum mechanics, some relationship between the spin and the statistics of identical particles has been postulated from the outset. But derivations of this spin-statistics relation have relied either on complicated relativistic field-theoretical methods, or on the existence of antiparticles. Berry and Robbins6 have now connected the spin and the statistics of identical particles without using either; and although the methods used in their work stray slightly outside the notions of standard quantum mechanics, they give us a new way of tackling an old problem.

In ordinary quantum mechanics, to quantize a system containing many identical particles, one uses the so-called symmetrization postulate: when any two particles' positions are exchanged, the wavefunction must either stay the same or change sign, that is, must be symmetric or antisymmetric. The former applies to bosons, particles with integer spin which obey Bose-Einstein statistics; the latter to fermions, which obey Fermi-Dirac statistics, that is, they conform to the exclusion principle (because if two particles are in the same quantum state, and they are exchanged, the wavefunction must remain the same). So far, there have been two somewhat different explanations.

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Figure 1: A simple way of visualizing the exchange of two particles is to take a rubber band and wrap it around your fingers so that the palm-si.
Figure 2: How the existence of antiparticles transforms an exchange into a rotation.

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  1. Theory and Laser Optics Groups, Blackett Laboratory, Imperial College, London, SW7 2BZ, UK

    Jason Twamley

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  1. Jason Twamley
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Twamley, J. Statistics given a spin. Nature 389, 127–129 (1997). https://doi.org/10.1038/38130

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