Abstract:
We successively apply the generalized Case–Foldy–Feshbach–Villars
(CFFV) and the Foldy–Wouthuysen (FW) transformation to
derive the Hamiltonian for relativistic scalar particles in
an electromagnetic field. In contrast to the original transformation,
the generalized CFFV transformation contains an arbitrary parameter and can be
performed for massless particles, which allows solving the problem of
massless particles in an electromagnetic field. We show that the form of
the Hamiltonian in the FW representation is independent of the arbitrarily chosen
parameter. Compared with the classical Hamiltonian for point particles, this
Hamiltonian contains quantum terms characterizing the quadrupole coupling of
moving particles to the electric field and the electric and mixed
polarizabilities. We obtain the quantum mechanical and semiclassical
equations of motion of massive and massless particles in an electromagnetic
field.
Citation:
A. Ya. Silenko, “Hamilton operator and the semiclassical limit for scalar particles in
an electromagnetic field”, TMF, 156:3 (2008), 398–411; Theoret. and Math. Phys., 156:3 (2008), 1308–1318
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Linking options:
https://www.mathnet.ru/eng/tmf6255
https://doi.org/10.4213/tmf6255
https://www.mathnet.ru/eng/tmf/v156/i3/p398
This publication is cited in the following 27 articles:
Alexander J. Silenko, “Leading correction to the relativistic Foldy-Wouthuysen Hamiltonian”, Phys. Rev. A, 111:3 (2025)
Alexander J Silenko, “Foldy-Wouthuysen transformation and multiwave states of a graphene electron in external fields and free (2+1)-space”, Phys. Scr., 99:2 (2024), 025905
A. Boumali, A. Hamla, Y. Chargui, “Determination of Shannon entropy and Fisher information of the Feshbach-Villars oscillator for spin-0 particles”, Int J Theor Phys, 63:8 (2024)
Ilyas Haouam, “Non-Relativistic Limit of Duffin-Kemmer-Petiau Equation in the Context of Magueijo-Smolin Model of the Doubly Special Relativity”, Int J Theor Phys, 63:8 (2024)
Abdelmalek Bouzenada, Abdelmalek Boumali, Edilberto O. Silva, “Applications of the Klein–Gordon equation in the Feshbach–Villars representation in the non-inertial cosmic string space–time”, Annals of Physics, 458 (2023), 169479
Abdelmalek Bouzenada, Abdelmalek Boumali, “Statistical properties of the two dimensional Feshbach–Villars oscillator (FVO) in the rotating cosmic string space–time”, Annals of Physics, 452 (2023), 169302
Alexander J. Silenko, “Zitterbewegungof massless particles”, Phys. Rev. A, 105:6 (2022)
A. J. Silenko, “Exact quantum-mechanical equations for particle beams”, Mod. Phys. Lett. A, 37:16 (2022)
Campos M.G., Ospedal L.P.R., “Effective Theories and Non-Minimal Couplings in Low-Dimensional Systems”, Mod. Phys. Lett. A, 36:15 (2021), 2150099
Silenko A.J., “Hermiticity and Self-Adjointness in Quantum Mechanics”, Nonlinear Phenom. Complex Syst., 24:1 (2021), 84–94
E. V. Vakulina, V. V. Andreev, N. V. Maksimenko, “The radiation of a spin-free particle in the field of a plane electromagnetic wave”, Vescì Akademìì navuk Belarusì. Seryâ fizika-matematyčnyh navuk, 57:4 (2021), 455
Zou L. Zhang P. Silenko A.J., “Position and Spin in Relativistic Quantum Mechanics”, Phys. Rev. A, 101:3 (2020), 032117
Silenko A.J., Xviii Workshop on High Energy Spin Physics, Dspin-2019, Journal of Physics Conference Series, 1435, IOP Publishing Ltd, 2020
Silenko A.J., Zhang P., Zou L., “Relativistic Quantum-Mechanical Description of Twisted Paraxial Electron and Photon Beams”, Phys. Rev. A, 100:3 (2019), 030101
Silenko A.J., “Relativistic Quantum Mechanics of a Proca Particle in Riemannian Spacetimes”, Phys. Rev. D, 98:2 (2018), 025014
Alexander J. Silenko, Pengming Zhang, Liping Zou, “Manipulating Twisted Electron Beams”, Phys. Rev. Lett., 119:24 (2017)
Silenko A.J., “Exact form of the exponential Foldy-Wouthuysen transformation operator for an arbitrary-spin particle”, Phys. Rev. A, 94:3 (2016), 032104
Boudjedaa B., Chetouani L., “Feynman Propagator for a Spinless Relativistic Particle in Feshbach?Villars Representation”, Rep. Math. Phys., 77:1 (2016), 69–86
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