Tepper L. Gill and W. W. Zachary
Foundations for Relativistic Quantum Theory I:
Feynman's Operator Calculus and the Dyson Conjectures
(292K, pdf)
ABSTRACT. In this paper, we provide a representation theory for the Feynman operator calculus. This allows us to solve the general initial-value problem and construct the Dyson series. We show that the series is asymptotic, thus proving Dyson's second conjecture for QED. In addition, we show that the expansion may be considered exact to any finite order by producing the remainder term. This implies that every non-perturbative solution has a perturbative expansion. Using a physical analysis of information from experiment verses that implied by our models, we reformulate our theory as a sum over paths. This allows us to relate our theory to Feynman s path integral, and to prove Dyson's second conjecture, that the divergences are in part due to a violation of Heisenberg's uncertainly relations.