## The Connection Between Spin and Statistics in Physical Review, Volume 58, Second Series, Number 8, October 15, 1940, pp. 716-723

Lancaster: The American Physical Society, 1940. 1st Edition. FIRST EDITION IN ORIGINAL WRAPS OF PAULI’S 1940 SPIN-STATISTICS RELATION PROOF. In 1939, the first spin-statistics relation was formulated by Swiss physicist Markus Fierz. Pauli rederived Fierz’s formula and his 1940 proof “. . has been the standard for almost sixty years” (Ian Duck & E. C. G. Sudarshan, Pauli and the spin-statistics theorem, 1998, p. x). “The explanation of the spin-statistics connection by Fierz and Pauli and by Luders and Zumino and by Burgoyne in the late 1950s ranks as one of the great triumphs of relativistic quantum field theory” (Zee, Quantum Field Theory, 2010).

The spin-statistics theorem relates particle spin to the particle statistics it obeys. “It clarifies one of the great mysteries of non-relativistic quantum theory: the contrasting symmetry properties of the wave functions of particles of integer (boson) versus half-integer (fermionic) spin” (Duncan, The Conceptual Framework, 2012).

Pauli first stated his exclusion principle in 1925, proposing “that electron states are defined using four quantum numbers, and no two electrons with the same set of quantum numbers can occupy the same electron shell” (History of Physics: The Wenner Collection). The 1940 paper offered here represents the completion of Pauli’s work on the exclusion principle, this because by demonstrating why fermions obey the principle by proving that integer spin particles are bosons, while half integer spin particles are fermions (the spin-statistics theorem)” (History of Physics: The Wenner Collection). Put another way, Pauli casts the exclusion principle as “a consequence of the spin-statistics theorem. What happens is that particles with a half-integer spin must have an antisymmetric wave function. This means that, if we exchange any two particles, the sign of the wave function must invert” (Yerle, A Physics Challenge).

'It was thinking about how to reconcile the Klein–Gordon and Dirac equations, and the existence of all these particles (how many more might be discovered?) that led Pauli to one of the most subtle concepts of modern physics — the spin–statistics theorem. In his 1940 paper, Pauli identified a vital connection between spin and quantum statistics… According to Pauli, particles of half-integer spin obey Fermi–Dirac statistics (and, hence, are now called 'fermions') and those of integer spin obey Bose–Einstein statistics ('bosons'). Mathematically speaking, the quantization of fields with half-integer spin relies on 'plus' commutation relations, whereas that of fields with integer spin uses 'minus' commutation relations.

“Put another way, the wave function of a system of bosons is symmetric if any pair of bosons is interchanged, but is antisymmetric for interchanged particles in a system of fermions. Subtle indeed, but from Pauli's spin–statistics connection arises the exclusion principle for fermions, with its implications for atomic structure, and a 'non-exclusion' principle for bosons — many bosons can adopt the same quantum state at once, as happens in a Bose–Einstein condensate. Further particle discoveries since 1940 and the subsequent building of the 'standard model' have also served to confirm that nature works with both integer and half-integer spins' (Alison Wright, 'Milestone 7 (1940): Spin–statistics connection', Milestones Timeline, 28 Feb. 2008, Nature Portal). Item #697

CONDITION & DETAILS: Original wraps. Lancaster: The American Physical Society. 4to (10.5 x 8 inches; 263 x 200mm). The slightest of toning at the edges of the wraps and pages. Near fine condition.

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