KINEMATICS AND HYDRODYNAMICS OF SPINNING PARTICLES

In the first part (Secs. I and II) of this paper, starting from the Pa uli current, we obtain the decomposition of the nonrelativistic field velocity into two orthogonal parts: (i) the ''classical'' part, that i s, the velocity w=p/m in the center of mass (c.m.), and (ii) the ''qua ntum'' 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) Lagran gian, we straightforwardly get the appearance of the so-called quantum potential associated, as it is known, with the Madelung fluid. This r esult provides further evidence of the possibility that the quantum be havior of microsystems is a direct consequence of the fundamental exis tence of spin. In the second part (Secs. III and IV), we fix our atten tion on the total velocity v=w+V, now necessarily considering relativi stic (classical) physics. We show that the proper time entering the de finition of the four-velocity upsilon(mu) for spinning particles has t o be the proper time tau of the c.m. frame. Inserting the correct Lore ntz factor into the definition of upsilon(mu) leads to completely diff erent kinematical properties for upsilon(2). The important constraint p (mu)upsilon(mu)=m, identically true for scalar particles but just as sumed a priori in all previous spinning-particle theories, is herein d erived in a self-consistent way. [S1050-2947(98)03701-9].