White Noise Calculus and Hamiltonian of a Quantum Stochastic Process

TL;DR

This paper develops a white noise quantum stochastic calculus using classical measure theory, establishes fundamental theorems, solves basic stochastic differential equations, and explicitly computes the Hamiltonian of the related quantum group.

Contribution

It introduces a novel white noise quantum stochastic calculus framework and explicitly derives the Hamiltonian for the associated quantum stochastic process.

Findings

Established Wick's and Ito's theorems in this calculus

Solved the simplest quantum stochastic differential equation

Explicitly calculated the Hamiltonian of the quantum group

Abstract

A white noise quantum stochastic calculus is developped using classical measure theory as mathematical tool. Wick's and Ito's theorems have been established. The simplest quantum stochastic differential equation has been solved, unicity and the conditions for unitarity have been proven. The Hamiltonian of the associated one parameter strongly continuous group has been calculated explicitely.