## Sound Relativistic Quantum Mechanics for a Strictly Solitary Nonzero-Mass Particle, and Its Quantum-Field Reverberations

**Authors:** Steven Kenneth Kauffmann

It is generally acknowledged that neither the Klein-Gordon equation nor the Dirac Hamiltonian can
produce sound solitary-particle relativistic quantum mechanics due to the ill effects of their negative-energy
solutions; instead their field-quantized wavefunctions are reinterpreted as dealing with particle and
antiparticle simultaneously - despite the clear physical distinguishability of antiparticle from particle and the
empirically known slight breaking of the underlying CP invariance. The natural square-root Hamiltonian
of the free relativistic solitary particle is iterated to obtain the Klein-Gordon equation and linearized to
obtain the Dirac Hamiltonian, steps that have calculational but not physical motivation, and which
generate the above-mentioned problematic negative-energy solutions as extraneous artifacts. Since the natural
square-root Hamiltonian for the free relativistic solitary particle contrariwise produces physically
unexceptionable quantum mechanics, this article focuses on extending that Hamiltonian to describe a solitary
particle (of either spin 0 or spin ½ in relativistic interaction with an external electromagnetic field. That
is achieved by use of Lorentz-covariant solitary-particle four-momentum techniques together with the
assumption that well-known nonrelativistic dynamics applies in the particle's rest frame. Lorentz-invariant
solitary-particle actions, whose formal Hamiltonization is an equivalent alternative approach, are as well
explicitly displayed. It is proposed that two separate solitary-particle wavefunctions, one for a particle
and the other for its antiparticle, be independently quantized in lieu of "reinterpreting" negative-energy
solutions - which indeed don't even afflict proper solitary particles.

**Comments:** 9 pages, Also archived as arXiv:0909.4025 [physics.gen-ph].

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### Submission history

[v1] 2 Dec 2009

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