This work presents a "Clean Quantum Theory of the Electron,"
based on Dirac s equation. "Clean" in the sense of a complete
mathematical explanation of the well known paradoxes of Dirac s
theory, and a connection to classical theory, including the motion
of a magnetic moment (spin) in the given field, all for a charged
particle (of spin 1/2) moving in a given electromagnetic field.
This theory is relativistically covariant, and it may be
regarded as a mathematically consistent quantum-mechanical
generalization of the classical motion of such a particle, a la
Newton and Einstein. Normally, our fields are time-independent, but
also discussed is the time-dependent case, where slightly different
features prevail. A "Schroedinger particle," such as a light
quantum, experiences a very different (time-dependent) "Precise
Predictablity of Observables." An attempt is made to compare both
cases.
There is not the Heisenberg uncertainty of location and momentum;
rather, location alone possesses a built-in uncertainty of
measurement.
Mathematically, our tools consist of the study of a
pseudo-differential operator (i.e. an "observable") under
conjugation with the Dirac propagator: such an operator has a
"symbol" approximately propagating along classical orbits, while
taking its "spin" along. This is correct only if the operator is
"precisely predictable," that is, it must approximately commute
with the Dirac Hamiltonian, and, in a sense, will preserve the
subspaces of electronic and positronic states of the underlying
Hilbert space."
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