Rotational Invariance and the Spin-Statistics Theorem

Abstract

In this article, the rotational invariance of entangled quantum states is investigated as a possible cause of the Pauli exclusion principle. First, it is shown that a certain class of rotationally invariant states can only occur in pairs. This is referred to as the coupling principle. This in turn suggests a natural classification of quantum systems into those containing coupled states and those that do not. Surprisingly, it would seem that Fermi–Dirac statistics follows as a consequence of this coupling while the Bose–Einstein follows by breaking it. In Sec. 5, the above approach is related to Pauli's original spin-statistics theorem and finally in the last two sections, a theoretical justification, based on Clebsch–Gordan coefficients and the experimental evidence respectively, is presented.

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O'Hara, P. Rotational Invariance and the Spin-Statistics Theorem. Foundations of Physics 33, 1349–1368 (2003). https://doi.org/10.1023/A:1025697412645

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  • rotational invariance
  • bosons
  • fermions
  • spin-statistics