Quantum phases for moving charges and dipoles in an electromagnetic field and fundamental equations of quantum mechanics

Abstract

We analyze the quantum phase effects for point-like charges and electric (magnetic) dipoles under a natural assumption that the observed phase for a dipole represents the sum of corresponding phases for charges composing this dipole. This way we disclose two novel quantum phases for charged particles, which we named as complementary electric Aharonov-Bohm (A-B) phase and complementary magnetic A-B phase, respectively. We reveal that these phases are derived from the Schrödinger equation only in the case, where 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 of charged particles. The related alteration should be introduced to Klein-Gordon and Dirac equations, too, and implications of this modification are discussed.

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

“…Hereinafter m (p) denotes the magnetic (electric) dipole moment, E(B) is the electric (magnetic) 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].…”

“…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 P EM for various physical problems (see, e.g., Ref. [3]). Now, we would like to point out an unfortunate error committed in [1] under determination of P EM 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.…”

“…The first and the second terms on the rhs of Eq. (10) correspond to the known electric and magnetic A-B phases [3], while the third and the firth terms stand respectively for the complementary electric and complementary magnetic A-B phases.…”

Quantum phases for electric charges and electric (magnetic) dipoles: physical meaning and implication

“…With respect to electrically bound quantum systems, in reference [27] we suggested the corresponding modification of fundamental equations of atomic physics with the suggested re-definition of the momentum operator (41), and have shown that this way promises the elimination of the available subtle deviations between calculated and measured data in precise physics of simple atoms.…”

Demystifying the nonlocality problem in Aharonov-Bohm effect

“…This may be relevant in the context of experiments trying to determine possible non-zero electric dipole moment of muon [27,28]. Kholmetskii et al [29] derived these additional quantum phases, other than the ones responsible for the Aharonov-Casher effect and the He-McKellar-Wilkens effect, using the covariant Lagrangian for the dipole in an electromagnetic field (assuming c = 1):…”