Quantum Physics


Fixing Dirac Theory's Relativity and Correspondence Errors

Authors: Steven Kenneth Kauffmann

Dirac sought a relativistic quantum free-particle Hamiltonian that imposes space-time symmetry on the Schroedinger equation in configuration representation; he ignored the Lorentz covariance of energy-momentum. Dirac free-particle velocity therefore is momentum-independent, breaching relativity basics. Dirac also made solutions of his equation satisfy the Klein-Gordon equation via requirements imposed on its operators. Dirac particle speed is thereby fixed to the unphysical value of c times the square root of three, and anticommutation requirements prevent four observables, including the components of velocity, from commuting when Planck's constant vanishes, a correspondence-principle breach responsible for Dirac free-particle spontaneous acceleration (zitterbewegung) that diverges in the classical limit. Nonrelativistic Pauli theory contrariwise is physically sensible, and its particle rest-frame action can be extended to become Lorentz invariant. The consequent Lagrangian yields the corresponding closed-form relativistic Hamiltonian when magnetic field is absent, otherwise a successive-approximation regime applies.

Comments: 11 Pages.

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Submission history

[v1] 2019-01-16 11:36:02
[v2] 2019-01-22 15:24:17 (removed)
[v3] 2019-01-26 08:40:07 (removed)
[v4] 2019-02-12 11:30:23 (removed)
[v5] 2019-02-14 01:24:38

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