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Journal of Neijiang Normal University

Analyses of the Electromagnetic Potentials

Xie Shi-chong

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

All sorts of elecrtomagnetic Potential are discussed.The range of applications of electric potenlial,magnetic scalar potential,vector potentiol,scalar potential,retarded potential,coulombic potential,electromagnetic potential are analysed,and point out their differences and relations. It is emphasized that retarded potential of kinetic charges is not quited right.The vector potential Ais a kind of physics reality,not only a mathematical method in quantum mechanics.The physics effect of A—AB effect can be obserred and measured.

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Journal of the Belarusian State University Physics•Feb 9, 2021•4 citations
All sorts of elecrtomagnetic Potential are discussed.The range of applications of electric potenlial,magnetic scalar potential,vector potentiol,scalar potential,retarded potential,coulombic potential,electromagnetic potential are analysed,and point out their differences and relations. It is emphasized that retarded potential of kinetic charges is not quited right.The vector potential Ais a kind of physics reality,not only a mathematical method in quantum mechanics.The physics effect of A—AB effect can be obserred and measured.
An explicit physical interpretation of the electromagnetic vector potential is here pointed out—as field momentum available for exchange with kinetic momenta of charged matter. It is shown that the vector potential can be quite as directly measurable, without recourse to only quantum-mechanical effects, as are scalar potential differences and the force fields E, B. This suggests, in keeping with quantum electrodynamics, that the equations for potentials may be regarded as more ’’basic’’ than the Maxwell equations—but only because the potentials most directly represent interaction energy-momenta through which fields and charges become observable.
The most popular interpretation of the Aharonov–Bohm (AB) effect is that the electromagnetic potential locally affects the complex phase of a charged particle’s wave function in the magnetic field free region. However, since the vector potential is a gauge-variant quantity, multiple researchers suspect that it is just a convenient tool for calculating the force field. This motivates them to explain the AB effect without using the vector potential, which inevitably leads to some sort of non-locality. This frustrating situation is shortly summarized by the statement by Aharonov et al. that the AB effect may be due to a local gauge potential or due to non-local gauge-invariant fields. In the present paper, we shall give several convincing arguments which support the viewpoint that the vector potential is not just a convenient mathematical tool with little physical entity. Despite its gauge arbitrariness, the vector potential certainly contains a gauge-invariant piece, which solely explains the observed AB phase shift. Importantly, this component has a property such that it is basically unique and cannot be eliminated by any regular gauge transformations. To complete the discussion, we also discuss the role of remaining gauge arbitrariness still contained in the entire vector potential.
Electromagnetic vector potential has physical significance in quantum mechanics as revealed by the Aharonov-Bohm effect for charged particles. However, till date it is thought that we cannot measure the vector potential directly as this is not a gauge invariant quantity. Contrary to this belief, here we show that one can indeed measure the electromagnetic vector potential using the notion of weak value. We show that it is simply the difference between the weak value of the canonical momentum of a charged particle in the presence and absence of magnetic field. This suggests that the vector potential is not only a physical entity but can be measured directly in the experiment.
We analyse the physical meaning of quantum phase effects for point-like charges and electric (magnetic) dipoles in an electromagnetic (EM) field. At present, there are known eight effects of such a kind: four of them (the magnetic and electric Aharonov – Bohm phases for electrons, the Aharonov – Casher phase for a moving magnetic dipole and the He – McKellar – Wilkens phase for a moving electric dipole) had been disclosed in 20th century, while four new quantum phases had recently been found by our team (A. L. Kholmetskii, O. V. Missevitch, T. Yarman). In our analysis of physical meaning of these phases, we adopt that a quantum phase for a dipole represents a superposition of quantum phases for each charge, composing the dipole. In this way, we demonstrate the failure of the Schrödinger equation for a charged particle in an EM field to describe new quantum phase effects, when the standard definition of the momentum operator is used. We further show that a consistent description of quantum phase effects for moving particles is achieved under appropriate re-definition of this operator, where the canonical momentum of particle in EM field is replaced by the interactional EM field momentum. Some implications of this result are discussed.