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

Abstract

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.

Quantum phase effects for electrically charged particles: Updated analysis

“…Thus, eq. ( 24), first obtained in [13,14] and named the "generalized de Broglie relationship", clearly clarifies the origin of the AB effect, where the observed phase difference over different paths of charge is explained by the corresponding difference in wavelengths over both paths, where the interactional EM field momentum P EM can be different. One can also see that eq.…”

“…Further on, combining eqs. (11) and (13), we obtain a new expression for the magnetic AB phase through the vector potential, resulting from eqs. ( 7), (8):…”

“…[1,2,15] by applying the heuristical SQP principle to quantum phases for dipoles, and was discussed in our recent publications (see e.g. [13,14]). Besides the evident advantage of being rigorous, present re-derivation through (7), (8) in the framework of the general quantum model [4] allows us to disclose more implications of eq.…”

Role of electromagnetic energy and momentum in the Aharonov–Bohm effect

“…obtained for the first time in [19] and named the generalized de Broglie relationship. Note that equations (3.1) and (3.6) ensure a straightforward interpretation of the magnetic AB effect: indeed, any circumference centred on the axis of the solenoid can be divided into two equal segments, where the interactional EM field momentum has opposite signs and, thus, the moving charged particle has different wavelengths (3.6) along these segments and, according to equation (3.1), acquires different phases.…”

“…Combining equations (3.1) and (3.4), we arrive at a compact presentation of the phase of a moving charged particle in the presence of an EM field as ϕfalse(bold-italicvfalse)=∫sktotal⋅ds, where k total is defined by equation (3.4). Hence, the wavelength of a moving charge in an EM field is given by the equation λfalse¯=ℏ|PM+PEM|, obtained for the first time in [19] and named the generalized de Broglie relationship.…”