Quantum phases for point-like charged particles and for electrically neutral dipoles in an electromagnetic field

A.L Kholmetskii,O.V Missevitch,T Yarman

doi:10.1016/j.aop.2018.03.005

A.L Kholmetskii, O.V Missevitch + Show 1 more

Open Access

https://doi.org/10.1016/j.aop.2018.03.005

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Abstract

We point out that the known quantum phases for an electric/magnetic dipole moving in an electromagnetic (EM) field must be presented as the superposition of more fundamental quantum phases emerging for elementary charges. Using this idea, we find two new fundamental quantum phases for point-like charges, next to the known electric and magnetic Aharonov–Bohm (A–B) phases, named by us as the complementary electric and magnetic phases, correspondingly. We further demonstrate that these new phases can indeed be derived via the Schrödinger equation for a particle in an EM field, where however the operator of momentum is re-defined via the replacement of the canonical momentum of particle by the sum of its mechanical momentum and interactional field momentum for a system “charged particle and a macroscopic source of EM field”. The implications of the obtained results are discussed.

Highlights

Three years ago, our paper [1] has been published, where we advanced the idea of explaining quantum phase effects for electric/ magnetic dipoles, expressed as the sum of four terms [1, 2]
Hereinafter m (p) denotes the magnetic dipole moment, E(B) is the electric field, v is the velocity, and ds=vdt is the path element. Developing this idea, we disclosed two new quantum phases for point-like charges – next to the known electric and magnetic Aharonov-Bohm (A-B) phases [3] – which we named as complementary electric and magnetic A-B phases, correspondingly [1]
We found that complementary A-B phases for electric charges can be described via fundamental equations of quantum mechanics only in the case [1], where we abandon the customary definition of the momentum operator via the canonical momentum Pc of a particle in an EM field, i.e

Summary

Pc eAc i

(Eq (30) of [1]), and adopt its new definition via the sum of the mechanical and interactional. The proposed redefinition of the momentum operator (2) has a number of important implications, and their analysis essentially depends on the particular expression for the interactional EM field momentum PEM for various physical problems We would like to point out an unfortunate error committed in [1] under determination of PEM for the system “point-like charged particle in an external EM field” as a function of the scalar and vector A potentials of the external EM field. Using the known expression for the interactional EM field momentum via the Poynting vector [5]

Be dV e

Lint e c