Kinematics and hydrodynamics of spinning particles

In the first part (Sections 1 and 2) of this paper --starting from the Pauli current, in the ordinary tensorial language-- we obtain the decomposition of the non-relativistic field velocity into two orthogonal parts: (i) the "classical part, that is, the 3-velocity w = p/m OF the center-of-mass (CM), and (ii) the so-called "quantum" part, that is, the 3-velocity V of the motion IN the CM 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 non-relativistic 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 carries further evidence that the quantum behaviour of micro-systems can be adirect consequence of the fundamental existence of spin. In the second part (Sections 3 and 4), we fix our attention on the total 3-velocity v = w + V, it being now necessary to pass to relativistic (classical) physics; and we show that the proper time entering the definition of the four-velocity v^mu for spinning particles has to be the proper time tau of the CM frame. Inserting the correct Lorentz factor into the definition of v^mu leads to completely new kinematical properties for v_mu v^mu. The important constraint p_mu v^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.Comment: LaTeX file; needs kapproc.st

On Locality in Quantum General Relativity and Quantum Gravity

The physical concept of locality is first analyzed in the special relativistic quantum regime, and compared with that of microcausality and the local commutativity of quantum fields. Its extrapolation to quantum general relativity on quantum bundles over curved spacetime is then described. It is shown that the resulting formulation of quantum-geometric locality based on the concept of local quantum frame incorporating a fundamental length embodies the key geometric and topological aspects of this concept. Taken in conjunction with the strong equivalence principle and the path-integral formulation of quantum propagation, quantum-geometric locality leads in a natural manner to the formulation of quantum-geometric propagation in curved spacetime. Its extrapolation to geometric quantum gravity formulated over quantum spacetime is described and analyzed.Comment: Mac-Word file translated to postscript for submission. The author may be reached at: [email protected] To appear in Found. Phys. vol. 27, 199