2ND-ORDER WAVE-EQUATION FOR SPIN-1/2 FIELDS .2. THE HILBERT-SPACE OF THE STATES

It is shown that, for spin-1/2 fields ruled by a second-order wave equation, it is possible to define a conserved current density whose zero component is positive definite. Hence one can (1) give a coherent statistical interpretation of the wave function, and (2) define a Hilbert space of the states with all the usual quantum-mechanical formalism. A new linearized form of the wave equation, completely equivalent to the second-order one, is finally presented. © 1986 The American Physical Society