On the relativistic theory of force-free particles with any spin

TL;DR

This paper discusses the quantum field theory of free particles with arbitrary spin, establishing their statistical behavior and analyzing the properties of their charge and energy densities, especially for higher spins.

Contribution

It demonstrates that integer-spin particles obey Bose statistics and half-integer-spin particles obey Fermi-Dirac statistics, and clarifies gauge invariance issues for higher-spin fields.

Findings

Particles with integer spin must have Bose statistics.

Particles with half-integer spin must follow Fermi-Dirac statistics.

Charge and energy densities are gauge invariant only in total for higher spins.

Abstract

In the free case, it is possible to define quantum fields which describe particles with integer or half-integer spin larger than one. It is shown that particles with integer spin must have Bose statistic and particles with half-integer-spin must follow Fermi-Dirac statistic. In the free case, the fields with spin smaller or equal to one are already well defined, so that for them alone, the charge and energy density are clearly identified and gauge invariant; while for the higher spin this is the case only for the total charge and total energy.