 06318 Tepper L Gill and Woodford W. Zachary
 CONSTRUCTIVE REPRESENTATION THEORY FOR THE
FEYNMAN OPERATOR CALCULUS
(613K, pdf)
Nov 6, 06

Abstract ,
Paper (src),
View paper
(auto. generated pdf),
Index
of related papers

Abstract. In this paper, we survey recent progress on the constructive
theory of the Feynman operator calculus. We first develop an operator
version of the HenstockKurzweil integral, and a new Hilbert space
that allows us to construct the elementary path integral in the manner
originally envisioned by Feynman. After developing our timeordered
operator theory we extend a few of the important theorems of semigroup
theory, including the HilleYosida theorem. As an application,
we unify and extend the theory of timedependent parabolic and hyperbolic
evolution equations. We then develop a general perturbation
theory and use it to prove that all theories generated by semigroups are
asympotic in the operatorvalued sense of Poincar e. This allows us to
provide a general theory for the interaction representation of relativistic
quantum theory. We then show that our theory can be reformulated
as a physically motivated sum over paths, and use this version to extend
the Feynman path integral to include more general interactions.
Our approach is independent of the space of continuous functions and
thus makes the question of the existence of a measure more of a natural
expectation than a death blow to the foundations for the Feynman
integral.
 Files:
06318.src(
06318.keywords ,
Generation Thoerems.pdf.mm )