Connecting Spin and Statistics in Quantum Mechanics

Abstract

Abstract. The spin-statistics connection is derived in a simple manner under the postulates that the original and the exchange wave functions are simply added, and that the azimuthal phase angle, which defines the orientation of the spin part of each single-particle spin-component eigenfunction in the plane normal to the spinquantization axis, is exchanged along with the other parameters. The spin factor (−1) 2s belongs to the exchange wave function when this function is constructed so as to get the spinor ambiguity under control. This is achieved by effecting the exchange of the azimuthal angle by means of rotations and admitting only rotations in one sense. The procedure works in Galilean as well as in Lorentz-invariant quantum mechanics. Relativistic quantum field theory is not required.

First quantized electrodynamics

“…Indeed, the single-particle, spin-1/2 Pauli wave equation [15] is covariant with respect to SO(3) provided that the electric potential A and the magnetic field B are functions of |x| alone. The spin-statistics connection has furthermore been proved for both nonrelativistic and relativistic quantum mechanics of arbitrary spin [14]. The proof takes into account the phases of spin eigenstates.…”

“…Unrestricted entanglement in space-time is shown to be an explicit contingency in the parametrized formalism. The spinstatistics connection has been proved by Jabs [14] using first quantization, and the line of proof is very briefly described here. Two-particle scattering is defined in terms of Møller operators, which lead without further conjecture to the Bethe-Salpeter equation.…”

Spin-Statistics Connection for Relativistic Quantum Mechanics

“…There is an elementary proof in nonrelativistic quantum mechanics for the spin-statistics connection [7]. The objective of this investigation is an elementary extension of the proof to the relativistic regime, using the parametrized Dirac equation attributed to Feynman and others [8].…”

Proposed physical explanation for the electron spin and related antisymmetry

“…As discussed in Ref. [12], one must take care that the rotations that take particle 1 to the azimuthal angle of particle 2 and vice versa, are both made in the same sense -say clockwise. When ϕ 2 > ϕ 1 , ϕ 1 transforms into ϕ 2 and ϕ 2 transforms into 2π + ϕ 1 , so that one gets…”

“…These two most prominent features of the electron are customarily taken in nonrelativistic quantum mechanics as empirical facts. Nevertheless, the concept of spin as a derived quality rather than an innate one has given rise over the years to a diversity of suggestive proposals, as is illustrated by our short but multifarious selection of relevant work [1]- [12]. On the other hand, despite the various proofs existing in the literature, the physical gears behind the spin-statistics connection are still unclear ( [10]- [11] and references therein).…”