Authors: Steven Kenneth Kauffmann
A single-particle Hamiltonian independent of the particle's coordinate ensures the particle conserves momentum, i.e., is free. This free-particle Hamiltonian is completely determined by Lorentz covariance of its energy-momentum and the particle's rest-energy value; such a free particle has velocity which vanishes when its momentum vanishes. Dirac required his free-particle Hamiltonian to be inhomogeneously linear in momentum, which contrariwise produces velocity that is independent of momentum; he also required his Hamiltonian's square to equal the above relativistic Hamiltonian's square, forcing many observables to anticommute and breach the quantum correspondence principle, as well as forcing the speed of any Dirac "free particle" to be c times the square root of three, which remains true when the particle interacts electromagnetically. The quantum correspondence principle breach causes a Dirac "free particle" to exhibit spontaneous acceleration that becomes unbounded in the classical limit; an artificial "spin" is also made available. Unlike the Dirac Hamiltonian, the nonrelativistic Pauli Hamiltonian is free of unphysical anomalies. Its relativistic extension is worked out via Lorentz-invariant upgrade of its associated action functional at zero particle velocity, and is obtained in closed form when there is no applied magnetic field; when there is, a successive approximation scheme must be used.
Comments: 12 Pages.
[v1] 2018-10-07 11:09:53
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