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The European Physical Journal Plus

Quantum phase effects for electrically charged particles: converging descriptions via fields and potentials

Alexander L. Kholmetskii, O. Missevitch, Tolga Yarman

Published Mar 1, 2022• 7 citations
Publisher
DOI
10.1140/epjp/s13360-022-02590-1

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QUANTUM MECHANIS OF ELECTRICALLY CHARGED PARTICLES

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•Jan 1, 1976•0 citations
Abstract We analyze the physical meaning of quantum phases for moving electric/magnetic dipoles through a superposition of quantum phases for point-like charges of the dipole, and in this way we disclose two new quantum phases for moving charges, next to the well-known magnetic and electric Aharonov-Bohm phases. We find that a consistent description of the full set of quantum phase effects for charged particles requires to modify the standard definition of the momentum operator via the canonical momentum of a particle towards a more inclusive definition, where this operator is associated with the vector sum of mechanical and interactional electromagnetic (EM) momenta for a charged particle in the EM field. Some principal implications of this result are discussed.
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.
The gauge invariance of the Aharonov-Bohm (AB) effect with a quantum treatment for the electromagnetic field is demonstrated. We provide an exact solution for the electromagnetic ground energy due to the interaction of the quantum electromagnetic field with the classical charges and currents that act as sources of the potentials in a classical description, in the Lorenz gauge. Then, we use first-order perturbation theory to compute an extra change on the electromagnetic ground energy due to the presence of a quantum charged particle with known wave function in the system. This energy in general depends on the quantum particle path in an interferometer, which results in an AB phase difference between the paths. The gauge invariance of this AB phase difference is then shown for the magnetic, electric, and the recently proposed electrodynamic versions of the AB effect. However, the AB phase difference could depend on the gauge for nonclosed paths, which reinforces the view that it only can be measured in closed paths.