Connecting Spin and Statistics in Quantum Mechanics
Abstract
The spinstatistics 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 singleparticle spincomponent eigenfunction in the plane normal to the spinquantization axis, is exchanged along with the other parameters. The spin factor (1)^{2 s } 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 Lorentzinvariant quantum mechanics. Relativistic quantum field theory is not required.
 Publication:

Foundations of Physics
 Pub Date:
 July 2010
 DOI:
 10.1007/s1070100993514
 arXiv:
 arXiv:0810.2399
 Bibcode:
 2010FoPh...40..776J
 Keywords:

 Spin and statistics;
 Spinor;
 Spinor ambiguity;
 Bose and Fermi statistics;
 Pauli exclusion principle;
 Symmetrization;
 Quantum Physics;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory
 EPrint:
 13 pages, Latex2e, considerably simplified version