Abstract
A class of field theories that are invariant under the complete Lorentz and gauge groups is discussed. These theories employ wave fields that provide irreducible representations of the space rotation group, so that the particles described by them have a definite spin. The Pauli-Weisskopf and Dirac theories are of this type, and apart from them there is just one theory for each value of the spin $\ensuremath{\geqq}\frac{1}{2}$ (the present theory for spin \textonehalf{} is different from the Dirac theory). There are in each of these cases four states of the field for a given momentum and spin orientation: both signs of energy and both signs of charge. Quantization according to the exclusion principle can be made to result in a positive definite energy, but this prevents the charge densities from commuting outside the light cone. It seems therefore that these theories do not correspond to reality.
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