## Unique Relativistic Extension of the Pauli Hamiltonian

**Authors:** Steven Kenneth Kauffmann

Relativistic extension of the Pauli Hamiltonian is ostensibly achieved by minimal coupling of electromagnetism to the free-particle Dirac Hamiltonian. But the free-particle Pauli Hamiltonian is pathology-free in its nonrelativistic domain, while the free-particle Dirac Hamiltonian yields completely fixed particle speed which is greater than c, spin orbit torque whose ratio to kinetic energy tends to infinity in the zero-momentum limit, and mega-violation of Newton's First Law in that limit. Furthermore, relativistic extension of the Pauli Hamiltonian is unique in principle because inertial frame hopping can keep the particle nonrelativistic. That extension is indeed readily achieved by upgrading the terms of the Pauli Hamiltonian's
corresponding action to appropriate Lorentz invariants. The resulting relativistic Lagrangian yields a canonical momentum that can't be analytically inverted in general, but a physically-sensible successive-approximation scheme applies. For hydrogen and simpler systems approximation isn't needed, and the result, which includes spin-orbit coupling, is as transparently physically sensible as the relativistic Lorentz Hamiltonian is, a far cry from the Dirac Hamiltonian pathologies.

**Comments:** 11 Pages.

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### Submission history

[v1] 2017-07-08 07:03:51 (removed)

[v2] 2017-07-09 06:45:20 (removed)

[v3] 2017-07-09 07:03:19 (removed)

[v4] 2017-07-11 10:14:46 (removed)

[v5] 2017-07-13 07:44:49 (removed)

[v6] 2017-07-13 13:14:05

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