Kinematics and hydrodynamics of spinning particles

In the first part (Secs. I and II) of this paper, starting from the Pauli current, we obtain the decomposition of the nonrelativistic field velocity into two orthogonal parts: (i) the "classical" part, that is, the velocity w=p/m in the center of mass (c.m.), and (ii) the "quantum'' part, that is, the velocity V of the motion of the c.m. frame (namely, the internal "spin motion" or Zitterbewegung). By inserting such a complete, composite expression of the velocity into the kinetic-energy term of the nonrelativistic classical (i.e., Newtonian) Lagrangian, we straightforwardly get the appearance of the so-called quantum potential associated, as it is known, with the Madelung fluid. This result provides further evidence of the possibility that the quantum behavior of microsystems is a direct consequence of the fundamental existence of spin. In the second part (Secs. III and IV), we fix our attention on the total velocity v=w+V, now necessarily considering relativistic (classical) physics. We show that the proper time entering the definition of the four-velocity upsilon(mu) for spinning particles has to be the proper time tau of the c.m. frame. Inserting the correct Lorentz factor into the definition of upsilon(mu) leads to completely different kinematical properties for upsilon(2). The important constraint p (mu)upsilon(mu)=m, identically true for scalar particles but just assumed a priori in all previous spinning-particle theories, is herein derived in a self-consistent way. [S1050-2947(98)03701-9].