New framework for the Feynman path integral

Sonia Mazzucchi

Vassili Nikitich Kolokoltsov

Yoshiteru Ishida

This paper proposes a framework for a new quantum computation based on the Feynman's path integral. The Feynman's path integral has been studied in quantum physics, however, the computational machinery may be used in universal computations. The light path design will be done in a light geometric automaton. As examples, we will present the primality test of an integer (for the deterministic case of light particle) and the stable marriage problem (for the probabilistic case of light wave).

Sergio A Albeverio, Raphael J. Høegh-Krohn

Naoto Kumano‐go

We define new curvilinear integrals along paths of Feynman path integral. In order to define curvilinear integrals along paths on a path space, Ito integrals use initial points of line segments of broken line paths, and Stratonovich integrals use middle points of them. However, our new curvilinear integrals use classical curvilinear integrals along broken line paths. Therefore, the classical fundamental theorem of calculus holds in Feynman path integral.

Sakhile Nyembe

This paper introduces Quantumatics, a superposed operator framework that bypasses Hilbert space notation and is shown to be mathematically equivalent to Feynman's Path Integral Formulation.