Relativistic theory of particles with arbitrary intrinsic momentum,” Nuovo Cim. 9

Summary. -The author establishes wave equations for particles having arbitrary given intrinsic angular momentum. Such equations are linear in the energy and relativistically invariant. As is well known, Dirac's theory of the electron makes use of a four-component wave function. When slow movements are considered, two of the components acquire negligible values, while the remaining two, at least in a first approximation, satisfy the Schrödinger equation. In a similar fashion, a particle having intrinsic angular momentum s 2 , . . .) is described in quantum mechanics by a set of 2s + 1 wave functions which separately satisfy the Schrödinger equation. Of course, such a representation is valid as long as the relativistic effects are neglected, and this is allowed for a particle moving with speed much smaller than the speed of light. A different case in which the elementary theory retains its validity is, of course, the one in which the velocity of the particle is comparable with c but remains approximately constant in direction and magnitude. In fact, this case can be reduced to the study of slow movements by means of a suitable choice of the frame of reference. ( *