FOUNDATIONS: RELATIVISTIC QUANTUM THEORY I MATHEMATICAL THEORY.

This is the first of a series on the foundations of quantum electrodynamics (QED). We first prove that: Minkowski's postulate is incompatible with the first postulate for two particles; analytic analysis of Dirac's equation leads to a new particle antiparticle separation, which reveals its time nonlocal nature; this also shows that the Pauli approximation is invalid for s-states and cut-offs are required before QED. We show Dirac's equation is not equivalent to the square root equation but is related by a unitary map. We then design the correct Hilbert space K S2 [Rn], for Feynman's path integral formulation of quantum theory and show it is not equivalent to L2 [Rn], the one for the Schodinger formulation, but is related by a unitary map. We also prove the existence of a universal clock and Santilli's dual of the real numbers to justify Feynman's v iew of antiparticles as particles going backwards in proper time. A major outcome of this study is that mathematical equivalence is not the same as physical equivalence and, careful physical analysis should be made before acceptance of mathematical concepts into physical theory. [ABSTRACT FROM AUTHOR]