A White Noise Approach to Phase Space Feynman Path Integrals

TL;DR

This paper introduces a white noise analysis method for phase space Feynman path integrals, successfully deriving quantum solutions like the harmonic oscillator while satisfying fundamental physics principles.

Contribution

It develops a novel white noise approach to phase space Feynman integrals, explicitly constructing integrands and generating functionals that reproduce quantum physics accurately.

Findings

Successfully reproduces Schrödinger equation solutions

Satisfies canonical commutation relations

Provides a rigorous mathematical framework

Abstract

The concepts of phase space Feynman integrals in White Noise Analysis are established. As an example the harmonic oscillator is treated. The approach perfectly reproduces the right physics. I.e., solutions to the Schr\"odinger equation are obtained and the canonical commutation relations are satisfied. The later can be shown, since we not only construct the integral but rather the Feynman integrand and the corresponding generating functional.