Interactions of massless particles of arbitrary spin

Abstract

The self-consistency problem s arising when massless particles of higher spin are coupled to the electromagnetic and gravitational fields are investigated using a group theoretic method as opposed to the Lagrangian approach employed by Fierz & Pauli (1939) in their discussion for massive particles. A massless particle of spin j is described by a 4j dimensional vector satisfying a generalization of Rumer’s equation (1930). 2j + 1 of these 4j components form the conventional quantity associated with a particle of spin j and the remaining 2j — 1 are supernumary quantities needed for the consistency of the in teracting system ; the whole object transforms according to the reduced representation (j, 0)⊕ (j — 1, 0) of the homogeneous Lorentz group. It is suggested that this formalismis a convenient way of writing higher-spin equations in particle-like form with attendant advantages (see, for example, Good 1959). In the force-free case the 2j — 1 auxiliary quantities can be set equal to zero but this is not possible in the interacting system with out inconsistency. One conclusion is that it is impossible for a (massless) particle of unique spin to be coupled minimally to gravitation unless either its spin is less than 1/2, space-time is conformally flat or its spin is two and it describes gravitation radiation itself.