## 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].

**Download:** **PDF**

### Submission history

[v1] 2 Dec 2009

**Unique-IP document downloads:** 148 times

**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.*

*
*