Reduced Spin-Statistics Theorem

TL;DR

This paper proposes a modified quantum theory framework where a single unitary irreducible representation describes both a particle and its antiparticle, leading to new insights on particle types, spins, and parity properties.

Contribution

It introduces a novel symmetry (AB symmetry) within the so(1,4) algebra framework, explaining fermionic nature and half-integer spins of elementary particles.

Findings

UIRs of so(1,4) can describe particles and antiparticles simultaneously

Elementary particles described by these UIRs are necessarily fermions

Vacuum conditions restrict elementary particles to half-integer spins

Abstract

As argued in our previous papers, it would be more natural to modify the standard approach to quantum theory by requiring that i) one unitary irreducible representation (UIR) of the symmetry algebra should describe a particle and its antiparticle simultaneously. This would automatically explain the existence of antiparticles and show that a particle and its antiparticle are different states of the same object. If i) is adopted then among the Poincare, so(2,3) and so(1,4) algebras only the latter is a candidate for constructing elementary particle theory. We extend our analysis in hep-th/0210144 and prove that: 1) UIRs of the so(1,4) algebra can indeed be interpreted in the framework of i) and cannot be interpreted in the framework of the standard approach; 2) as a consequence of a new symmetry (called AB one) between particles and antiparticles for UIRs satisfying i), elementary particles described by UIRs of the so(1,4) algebra can be only fermions; 3) as a consequence of the AB symmetry, the vacuum condition can be consistent only for particles with the half-integer spin (in conventional units) and therefore only such particles can be elementary. In our approach the well known fact that fermions have imaginary parity is a consequence of the AB symmetry.