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It is generally acknowledged that neither the Klein-Gordon equation nor theDirac Hamiltonian can produce sound solitary-particle relativistic quantummechanics due to the ill effects of their negative-energy solutions; insteadtheir field-quantized wavefunctions are reinterpreted as dealing with particleand antiparticle simultaneously--despite the clear physical distinguishabilityof antiparticle from particle and the empirically known slight breaking of theunderlying CP invariance. The natural square-root Hamiltonian of the freerelativistic solitary particle is iterated to obtain the Klein-Gordon equationand linearized to obtain the Dirac Hamiltonian, steps that have calculationalbut not physical motivation, and which generate the above-mentioned problematicnegative-energy solutions as extraneous artifacts. Since the natural squareroot Hamiltonian for the free relativistic solitary particle contrariwiseproduces physically unexceptionable quantum mechanics, this article focuses onextending that Hamiltonian to describe a solitary particle (of either spin 0 orspin one-half) in relativistic interaction with an external electromagneticfield. That is achieved by use of Lorentz-covariant solitary-particle fourmomentum techniques together with the assumption that well-knownnonrelativistic dynamics applies in the particle's rest frame.Lorentz-invariant solitary particle actions, whose formal Hamiltonization is anequivalent alternative approach, are as well explicitly displayed. It isproposed that two separate solitary-particle wavefunctions, one for a particleand the other for its antiparticle, be independently quantized in lieu of"reinterpreting" negative energy solutions--which indeed don't even afflictproper solitary particles.

Sound relativistic quantum mechanics for a strictly solitary nonzero-mass particle, and its quantum-field reverberations