The Feynman integrand for the Charged Particle in a Constant Magnetic field as White Noise Distribution

TL;DR

This paper applies white noise analysis to rigorously construct the Feynman integrand for a charged particle in a constant magnetic field, representing it as a Hida distribution using generalized Gauss kernels.

Contribution

It introduces a novel approach to model the Feynman integrand as a Hida distribution within white noise analysis, specifically for a charged particle in a magnetic field.

Findings

Feynman integrand realized as a Hida distribution

Velocity dependent potential identified as generalized Gauss kernel

Provides a rigorous mathematical framework for quantum particle in magnetic fields

Abstract

The concepts of Feynman integrals in white noise analysis are used to realize the Feynman integrand for a charged particle in a constant magnetic field as a Hida distribution. For this purpose we identify the velocity dependent potential as a so called generalized Gauss kernel.