The Hamiltonian Path Integrand for the Charged Particle in a Constant Magnetic field as White Noise Distribution

TL;DR

This paper models the Hamiltonian Feynman integrand for a charged particle in a constant magnetic field as a white noise distribution, using white noise analysis to handle velocity-dependent potentials.

Contribution

It introduces a novel white noise distribution framework for the Hamiltonian Feynman integrand with velocity dependence in a magnetic field.

Findings

Realization of the Hamiltonian Feynman integrand as a Hida distribution.

Derivation of propagators and generating functionals.

Representation of velocity-dependent potential as a generalized Gauss kernel.

Abstract

The concepts of Hamiltonian Feynman integrals in white noise analysis are used to realize as the first velocity dependent potential the Hamiltonian Feynman integrand for a charged particle in a constant magnetic field in coordinate space as a Hida distribution. For this purpose the velocity dependent potential gives rise to a generalized Gauss kernel. Besides the propagators also the generating functionals are obtained.