Connecting spin and statistics in quantum mechanics
arXiv:0810.2399 · doi:10.1007/s10701-009-9351-4 10.1007/s10701-009-9377-7
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 spin-quantization 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.
13 pages, Latex2e, considerably simplified version
References in corpus (6)
- Spin and Statistics in Nonrelativistic Quantum Mechanics: The Zero Spin Case
- Spin & Statistics in Nonrelativistic Quantum Mechanics, I
- Spin and Statistics in Classical Mechanics
- Non-relativistic proofs of the spin-statistics connection
- Spin & Statistics in Nonrelativistic Quantum Mechanics, II
- No spin-statistics connection in nonrelativistic quantum mechanics