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arXiv:1307.3478 · Infinite Dimensional Analysis Quantum Probability and Related Topics

The Hamiltonian path integrand for the charged particle in a constant magnetic field as white noise distribution

Wolfgang Böck, Martin Grothaus

Published Jun 1, 2015• 2 citations
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Abstract

The concepts of Hamiltonian Feynman integrals in white noise analysis are used to realize as the first velocity-dependent potential of 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, the generating functionals are obtained.

DOI
10.1142/s0219025715500101

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The concepts of Hamiltonian Feynman integrals in white noise analysis are used to realize as the first velocity-dependent potential of 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, the generating functionals are obtained.
The propagator for a charged particle in a time‐dependent electric field is calculated following Hida and Streit's framework [1] where the propagator is the T‐transform of Feynman functional. However, we have to regard the potential V = −qE(τ)x≡mℏξ̇x following C. C. Bernido and M. V. Carpio‐Bernido's [2] prescription of time‐dependent potentials. The result agrees with the limiting form of Eqn. (16) of N. Morgenstern Horing, H. L. Cui, and G. Fiorenza [3], when the magnetic field is switched off, and Eqn. (17) of [3] when the electric field is constant in time.