“…In this section we adopt for simplicity the weak relativistic limit, corresponding to the accuracy of calculations c −2 for electric effects and c −3 for magnetic effects. As is shown in refs 17 , 18 , in this limit the first four terms of eq. ( 5 ) can be presented in the convenient form where all quantities are defined in a labframe.…”
Section: Origin Of Quantum Phase Effects For Electric/magnetic Dipolesupporting
confidence: 55%
“…( 10 ) derived for a moving dipole finds its physical interpretation via the corresponding fundamental phase for point-like charge, as is shown in Fig. 1 adapted from refs 17 , 18 . Figure 1 Relationship between quantum phases for charged particles and for moving dipoles.…”
Section: Origin Of Quantum Phase Effects For Electric/magnetic Dipolementioning
confidence: 72%
“…In ref. 18 we demonstrate that the term e A / c describes the momentum of interactional EM field P EM for a system “charged particle and a source of external EM field” in the particular case, where the particle rests in the laboratory frame, i.e. …”
Section: Quantum Phases and Hamiltonian Of Charged Particle In An Elementioning
confidence: 85%
“…Determining corresponding phases, we use the appropriate models of electric and magnetic dipoles. In particular, adopting the simplest model of electric dipole (two point-like charges − e and + e separated by a small distance d ), we find 17 , 18 that the third term of eq. ( 10 ) can be presented in the form …”
Section: Origin Of Quantum Phase Effects For Electric/magnetic Dipolementioning
confidence: 99%
“…Finally, for the last term on rhs of eq. ( 10 ), we derive 17 , 18 where j is the current density of carriers of current in the magnetic dipole m . We clarify the origin of the phase effect (13) for the charge e , moving along a circular orbit at some velocity v with the current density .…”
Section: Origin Of Quantum Phase Effects For Electric/magnetic Dipolementioning
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.
“…In this section we adopt for simplicity the weak relativistic limit, corresponding to the accuracy of calculations c −2 for electric effects and c −3 for magnetic effects. As is shown in refs 17 , 18 , in this limit the first four terms of eq. ( 5 ) can be presented in the convenient form where all quantities are defined in a labframe.…”
Section: Origin Of Quantum Phase Effects For Electric/magnetic Dipolesupporting
confidence: 55%
“…( 10 ) derived for a moving dipole finds its physical interpretation via the corresponding fundamental phase for point-like charge, as is shown in Fig. 1 adapted from refs 17 , 18 . Figure 1 Relationship between quantum phases for charged particles and for moving dipoles.…”
Section: Origin Of Quantum Phase Effects For Electric/magnetic Dipolementioning
confidence: 72%
“…In ref. 18 we demonstrate that the term e A / c describes the momentum of interactional EM field P EM for a system “charged particle and a source of external EM field” in the particular case, where the particle rests in the laboratory frame, i.e. …”
Section: Quantum Phases and Hamiltonian Of Charged Particle In An Elementioning
confidence: 85%
“…Determining corresponding phases, we use the appropriate models of electric and magnetic dipoles. In particular, adopting the simplest model of electric dipole (two point-like charges − e and + e separated by a small distance d ), we find 17 , 18 that the third term of eq. ( 10 ) can be presented in the form …”
Section: Origin Of Quantum Phase Effects For Electric/magnetic Dipolementioning
confidence: 99%
“…Finally, for the last term on rhs of eq. ( 10 ), we derive 17 , 18 where j is the current density of carriers of current in the magnetic dipole m . We clarify the origin of the phase effect (13) for the charge e , moving along a circular orbit at some velocity v with the current density .…”
Section: Origin Of Quantum Phase Effects For Electric/magnetic Dipolementioning
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.
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