Quantum Physics


The Dirac Hamiltonian's Egregious Violations of Special Relativity; the Nonrelativistic Pauli Hamiltonian's Unique Relativistic Extension

Authors: Steven Kenneth Kauffmann

A single-particle Hamiltonian independent of the particle's coordinate ensures the particle conserves momentum, i.e., is free. Lorentz-covariance of that Hamiltonian's energy-momentum specifies it up to the particle's rest energy; the free particle it describes has speed below c and constant velocity parallel to its conserved momentum. Dirac took his free-particle Hamiltonian to have the same squared value as that relativistic one, but unwittingly blocked Lorentz-covariance of his Hamiltonian's energy-momentum by requiring it to be inhomogeneously linear in momentum. The Dirac "free particle" badly flouts relativity and even physical cogency; its velocity direction is extremely nonconstant, while its speed is fixed to c times the square root of three even when it interacts electromagnetically. Both its rest energy and total energy can be negative, and its velocity components and rest energy are artificially correlated by being mutually anticommuting; its alleged "spin" is an artifact of the anticommutation of its velocity components. Unlike the Dirac Hamiltonian, the nonrelativistic Pauli Hamiltonian is apparently physically sensible for particle speed far below c. 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 if there is no applied magnetic field; a successive approximation scheme must otherwise be used.

Comments: 13 Pages.

Download: PDF

Submission history

[v1] 2018-09-15 17:24:23
[v2] 2018-09-17 22:31:49 (removed)
[v3] 2018-09-22 16:18:53

Unique-IP document downloads: 74 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus