Group theory of massless Boson fields

Abstract

Free massless Boson fields are defined as manifestly covariant unitary representations of the Poincaré group for zero mass and integer spin s . The fields are tensors which, in the simplest case, belong to the representationD(s,0) ⊕ D(0,s) of the Lorentz group. They are characterized by wave equations of two types: (i) The symmetry conditions, which impose the requirement that the tensors indeed carry the representation D(s,0) ⊕ D(0,s), and(ii) the unitarity conditions, which turn out to be of the form {im573-1}

In the case s = 2 the field is a 4th rank tensor, the symmetry conditions are the equations of the Riemann curvature tensor in the linearized vacuum theory of gravitation, and the unitarity conditions are the Bianchi identities.