Trajectory-state theory of the Klein-Gordon field

Abstract

We develop a trajectory construction of solutions to the massless wave equation in n+1 dimensions and hence show that the quantum state of a massive relativistic system in 3+1 dimensions may be represented by a stand-alone four-dimensional congruence comprising a continuum of 3-trajectories coupled to an internal scalar time coordinate. A real Klein-Gordon amplitude is the current density generated by the temporal gradient of the internal time. Complex amplitudes are generated by a two-phase flow. The Lorentz covariance of the trajectory model is established.

10 pages.; footnote 4 added, results unchanged

References in corpus (2)

• Three-dimensional representation of the many-body quantum state
• On systems having Poincaré and Galileo symmetry

Cited by in corpus (3)

• Relativistic Bohmian trajectories and Klein-Gordon currents for spin-0 particles
• Trajectory construction of Dirac evolution
• Eliminating the wavefunction from quantum dynamics: the bi-Hamilton-Jacobi theory, trajectories and time reversal