Abstract
A theory of covariant wave equations for massless particles is set up, based on wave functions transforming according to the finite-dimensional nonunitary representations ( ab) of the homogeneous Lorentz group. For each λ = − a − b, − a − b + 1, …, a + b, there are sets of covariant subsidiary conditions which, subject to generalized gauge invariance, guarantee that the wave functions describe only particles of zero mass and helicity λ, and that an invariant scalar product exists, under which the representation of the inhomogeneous Lorentz group is unitary as well as irreducible. In this way it is proved that there are infinitely many covariant theories for a massless particle with any given helicity, and a procedure for constructing any such theory is given. The representations are extended to include negative energy, and a Foldy-Wouthuysen transformation derived. It is shown how to give covariant definitions of space and time inversion in the theory.
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