Quantum Stochastic Paths and Stochastic Differential Equations

Franco Fagnola

Corentin Perret-Gentil, W. P. Petersen

Path integral representations of quantum dynamics can often be formulated as stochastic differential equations (SDEs).In a series of papers, Corney and Drummond (2004

Wako Takanashi

Stochastic differentials in stochastic differential equations are defined by Ito integrals, however if stochastic differentials and stochastic variations are defined in a mechanical engineering field more better.In this paper, stochastic differentiation as a difference due to distributed time is defined, and clarify its relationship with tensor products and renormalization groups in engineering.The examine the meaning of the Rough path as tensor product , and are obtained the Uncertainty principle in quantum mechanics due to the Rough path based on the renormalization group due to this rough path. Furthermore, the quantum gravity equation is obtained from the rough pass theory.

J. Martin Lindsay, Adam Skalski

Toshihiko Arimitsu, Takeshi Saito

M O'Connor

The author gives an explicit relation between the path integral and the operator ordering of the Hamiltonian for supersymmetric quantum mechanics. Using a stochastic differential equation the author is able to resolve the ambiguities associated with defining the supersymmetric path integral.