Only Fermions Can Be Elementary

In standard Poincare and anti de Sitter SO(2,3) invariant theories, the existence of antiparticles is explained by using the fact that covariant equations have solutions with negative energies. In these theories a particle and its antiparticle are described by independent positive energy irreducible representations (IRs) of the symmetry group. Such an approach cannot be applied in de Sitter SO(1,4) invariant theory. As argued in our previous papers, it would be more natural to require that i) one IR 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, with such a modification of the standard approach, among the above groups only the SO(1,4) one is a candidate for constructing elementary particle theories. We investigate unitary IRs of this group and show that they indeed can be interpreted in the framework of i). By quantizing such IRs and requiring that the energy should be positive in the limit when the SO(1,4) group can be contracted to the Poincare one, we conclude that only fermions can be elementary particles. PACS: 11.30Cp, 11.30.Ly 1 The statement of the problem In standard quantum theory the existence of antiparticles is explained as follows. Each elementary particle can be described in two ways: i) by