Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1511.04341 · Europhysics Letters (EPL)

Force law in material media and quantum phases

Alexander Kholmetskii, Oleg Missevitch, Tolga Yarman

Published Jan 1, 2016• 20 citations
arXivHTMLPDF

Abstract

We show that the known expressions for the force on a point-like dipole are incompatible with the relativistic transformation of force, and in this respect we apply the Lagrangian approach to the derivation of the correct equation for force on a small electric/magnetic dipole. The obtained expression for the generalized momentum of a moving dipole predicts two novel quantum effects with non-topological and non-dynamic phases, when an electric dipole is moving in an electric field, and when a magnetic dipole is moving in a magnetic field, respectively.

DOI
10.1209/0295-5075/113/14003

Related papers

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

Alexander L. Kholmetskii, O. Missevitch, Tolga Yarman

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.

Journal of the Belarusian State University Physics•Feb 9, 2021•4 citations

Effective Interaction Force between an Electric Charge and a Magnetic Dipole and Locality (or Nonlocality) in Quantum Effects of the Aharonov–Bohm Type

Gianfranco Spavieri, George T. Gillies, Miguel Rodriguez +1 more

Classical electrodynamics foresees that the effective interaction force between a moving charge and a magnetic dipole is modified by the time-varying total momentum of the interaction fields. We derive the equations of motion of the particles from the total stress-energy tensor, assuming the validity of Maxwell’s equations and the total momentum conservation law. Applications to the effects of Aharonov–Bohm type show that the observed phase shift may be due to the relative lag between interfering particles caused by the effective local force.

arXiv:2005.05796•Chinese Physics Letters•Mar 1, 2021•6 citations

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

Alexander L. Kholmetskii, Tolga Yarman, O. Missevitch +1 more

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.

Scientific Reports•Aug 3, 2018•15 citations

Quantum phase effects for electrically charged particles and redefinition of the momentum operator

Alexander L. Kholmetskii, Tolga Yarman, O. Missevitch

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.

Journal of Physics Conference Series•Mar 1, 2022•1 citation

Quantum phases for a charged particle and electric/magnetic dipole in an electromagnetic field

Alexander L. Kholmetskii, Tolga Yarman

We point out that the known quantum phases for an electric/magnetic dipole moving in an electromagnetic field must be composed from more fundamental quantum phases emerging for moving elementary charges. Using this idea, we have found two new fundamental quantum phases, next to the known magnetic and electric Aharonov-Bohm phases, and discuss their general properties and physical meaning.

Europhysics Letters (EPL)•Nov 1, 2017•16 citations

Classical and Quantum Interaction of the Dipole Revisited

Tomislav Ivezić

The interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is investigated in an approach that deals with four-dimensional (4D) geometric quantities. The new commutation relations for the 4D orbital and intrinsic angular momentums and also for the 4D dipole moments are introduced. The expectation value of the quantum 4-force, which holds in any frame, is worked out in terms of them. In contrast to it the whole calculation in [1] ([1] J. Anandan, Phys. Rev. Lett. \textbf{85}, 1354 (2000)) has been made only in the rest frame of the dipole. It is proved that, e.g., the expression for the 3D force $\mathbf{f}%_{S}$ in [1] is not relativistically correct and that the quantum 4-force is not zero in the experiments proposed in [1]. This means that the phase shifts that could be observed in such experiments are not topological phase shifts.

arXiv:0705.0744•May 5, 2007•0 citations
We show that the known expressions for the force on a point-like dipole are incompatible with the relativistic transformation of force, and in this respect we apply the Lagrangian approach to the derivation of the correct equation for force on a small electric/magnetic dipole. The obtained expression for the generalized momentum of a moving dipole predicts two novel quantum effects with non-topological and non-dynamic phases, when an electric dipole is moving in an electric field, and when a magnetic dipole is moving in a magnetic field, respectively.
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.
Classical electrodynamics foresees that the effective interaction force between a moving charge and a magnetic dipole is modified by the time-varying total momentum of the interaction fields. We derive the equations of motion of the particles from the total stress-energy tensor, assuming the validity of Maxwell’s equations and the total momentum conservation law. Applications to the effects of Aharonov–Bohm type show that the observed phase shift may be due to the relative lag between interfering particles caused by the effective local force.
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.
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.
The interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is investigated in an approach that deals with four-dimensional (4D) geometric quantities. The new commutation relations for the 4D orbital and intrinsic angular momentums and also for the 4D dipole moments are introduced. The expectation value of the quantum 4-force, which holds in any frame, is worked out in terms of them. In contrast to it the whole calculation in [1] ([1] J. Anandan, Phys. Rev. Lett. \textbf{85}, 1354 (2000)) has been made only in the rest frame of the dipole. It is proved that, e.g., the expression for the 3D force f\mathbf{f}%_{S}f in [1] is not relativistically correct and that the quantum 4-force is not zero in the experiments proposed in [1]. This means that the phase shifts that could be observed in such experiments are not topological phase shifts.