  This paper is a progress report on the foundations for the canonical
proper-time approach to relativistic quantum theory. We first review the the
standard square-root equation of relativistic quantum theory, followed by a
review of the Dirac equation, providing new insights into the physical
properties of both. We then introduce the canonical proper-time theory. For
completeness, we give a brief outline of the canonical proper-time approach to
electrodynamics and mechanics, and then introduce the canonical proper-time
approach to relativistic quantum theory. This theory leads to three new
relativistic wave equations. In each case, the canonical generator of
proper-time translations is strictly positive definite, so that it represents a
particle. We show that the canonical proper-time extension of the Dirac
equation for Hydrogen gives results that are consistently closer to the
experimental data, when compared to the Dirac equation. However, these results
are not sufficient to account for either the Lamb shift or the anomalous
magnetic moment.
