In this paper, we report on a new approach to relativistic quantum theory.
The classical theory is derived from a new; implementation of the first two
postulates of Einstein, which fixes the proper-time of the physical system
of interest for all observers. This approach leads to a new group that ive
call the proper-time group. We then construct a canonical contact transfor
mation on extended phase space to identify the canonical Hamiltonian associ
ated with the proper-time variable. On quantization Ive get a new relativis
tic wave equation for spin 1/2 particles that generalizes the Dirac theory.
The Hamiltonian is positive definite so Ive naturally interpret antipartic
les as particles with their proper-time reversed. I We show that for the hy
drogen atom problem, we get the same fine structure separation. When the pr
oton spin magnetic moment is taken into account, we get the standard hyperf
ine splitting terms of the Pauli approximation and two additional terms. Th
e first term is small in p-states. It diverges in s-states, and provides mo
re than enough to account for the Lamb-shift when the proton radius is used
as a cut off The last term promises to provide a correction to the hyperfi
ne splitting term. Although incomplete, the general approach offers hope of
completely accounting for the hydrogen spectrum as an eigenvalue problem.