Particles with Half-Integer Spin

Harley D. Scammell

Bipin R. Desai

Randall G. Hulet

At the quantum level, particles behave very differently depending on whether their spin angular momentum is an integer or a half integer. Half-integer spin particles are known as fermions, and include all the constituents of atoms: electrons, protons and neutrons. Bosons, on the other hand, are particles with integer spin, such as photons.

P. M. Mathews

It is shown that a recently derived relativistic Schr\"odinger equation for free particles of arbitrary spin can be consistently quantized in the case of half-integer spins (but not for integer spins) by invoking the microcausality condition and using the role of certain expectation values of the $c$-number theory as generators of transformations of the Poincar\'e group in the $q$-number theory. The correct type of statistics (Fermi-Dirac) for half-integer-spin particles is obtained as a consequence of the theory. The way to handle the integer-spin case is indicated, but details are left for future presentation.