Sophia University Institute
In previous work, the Hamiltonian Jacobi equation associated with the metrics of general relativity have been identified as a gen- eralized Dirac equation for quantum mechanics. This theory is now further devoloped to show its implications for the Zitterbewugung problem and its relationship to isotropy. Moreover, it is also shown that for the theory to be consistent, the momentum defined by the Hamilton-Jacobi function presupposes the existence of a universal paramenter in agreement with the Horwitz-Stueckeleberg theory. In the case of particles with mass this invariant parameter can be defined by where has the units of time and has the units of mass. For examples, for a particle trajectory parametrized by the proper time , the Hamilton-Jacobi formalism requires that , where is the rest mass.