Trajectory-state theory of the Klein-Gordon field
Green Templeton College, Oxford University, Oxford, UK
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Accepted: 9 August 2019
Published online: 9 September 2019
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.
© The Author(s), 2019