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.
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C. Truesdell, R.A. Toupin, in Handbuch der Physik, Band III/I, edited by S. Flügge (Springer-Verlag, Berlin, 1960)
A. Crisanti, M. Falcioni, A. Vulpiani, G. Paladin, Riv. Nuovo Cimento 14, 1 (1991)
P. Holland, Ann. Phys. (NY) 315, 503 (2005)
P. Holland, in Quantum Structural Studies, edited by R.E. Kastner (World Scientific, London, 2017)
P. Holland, Proc. R. Soc. A 461, 3659 (2005)
P. Holland, in Quantum Trajectories, edited by P. Chattaraj (Taylor & Francis/CRC, Boca Raton, 2010)
P. Holland, J. Mol. Model. 24, 269 (2018)
P. Holland, J. Phys. A 42, 075307 (2009)
H. Feshbach, F. Villars, Rev. Mod. Phys. 30, 24 (1958)
P.R. Holland, The Quantum Theory of Motion (Cambridge University Press, Cambridge, 1993)
P. Holland, Int. J. Theor. Phys. 51, 667 (2012)
P. Holland, Ann. Phys. (NY) 351, 935 (2014)
P. Holland, Ann. Phys. (Leipzig) 12, 446 (2003)
P. Holland, in Concepts and Methods in Modern Theoretical Chemistry: Statistical Mechanics, edited by S.K. Ghosh, P.K. Chattaraj (Taylor & Francis/CRC, Boca Raton, 2013)
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Holland, P. Trajectory-state theory of the Klein-Gordon field. Eur. Phys. J. Plus 134, 434 (2019). https://doi.org/10.1140/epjp/i2019-12922-5
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DOI: https://doi.org/10.1140/epjp/i2019-12922-5