Could Only Fermions Be Elementary?

TL;DR

This paper proposes a new perspective on elementary particles, suggesting that only fermions can be elementary and that particles and antiparticles are different states of the same object, based on de Sitter symmetry.

Contribution

It introduces a novel interpretation of unitary irreducible representations of SO(1,4) and argues that elementary particles must be fermions, explaining the absence of neutral elementary particles.

Findings

Elementary particles can only be fermions.

C invariance is not exact even in free massive theories.

Elementary particles cannot be neutral, explaining observed neutral bosons.

Abstract

In standard Poincare and anti de Sitter SO(2,3) invariant theories, antiparticles are related to negative energy solutions of covariant equations while independent positive energy unitary irreducible representations (UIRs) of the symmetry group are used for describing both a particle and its antiparticle. Such an approach cannot be applied in de Sitter SO(1,4) invariant theory. We argue that it would be more natural to require that (*) one UIR 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 (*) is adopted then among the above groups only the SO(1,4) one can be a candidate for constructing elementary particle theory. It is shown that UIRs of the SO(1,4) group can be interpreted in the framework of (*) and cannot be interpreted in the standard way. By quantizing such UIRs and requiring that the energy should be positive in the Poincare approximation, we conclude that i) elementary particles can be only fermions. It is also shown that ii) C invariance is not exact even in the free massive theory and iii) elementary particles cannot be neutral. This gives a natural explanation of the fact that all observed neutral states are bosons.