Abstract
As a possible basis for a unitary description of particles a new spinor wave equation is proposed which is similar to Heisenberg’s non-linear generalization of Dirac’s equation but exhibits in addition an invariance with respect to conformai transformations. A 2 x 2 matrix formalism is developed in view of obtaining a synthetic expression for conformai transformations as well as for spinor equations of Dirac’s type. A direct proof of the conform-invariance of the new equation is then given with the aid of this formalism and an explicit transformation law for the wave function is derived. It is further shown that the unquantized equation allows for the propagation of plane waves corresponding to particles of different rest masses.
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