Quantenelektrodynamik im Konfigurationsraum
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
For a spin-1 particle with a magnetic moment, taking into account quadrupole interactions leads to the FW Hamiltonian Eq. (61).
“For a spin-1 particle with a magnetic moment, taking into account quadrupole interactions [61,89] leads to the following FW Hamiltonian [89]:”
From <i>Zitterbewegung</i> of massless particles (2022) · cites this paper as [61]
Cites
Still being checked.
Cited by
Sorted by citations
Fermi, E. (1932) · Reviews of Modern Physics · doi:10.1103/revmodphys.4.87 · Cited by 1,134 · see citing works
Die allgemeinen Prinzipien der Wellenmechanik
Pauli, W. E. F. (1933) · Springer eBooks · doi:10.1007/978-3-642-52619-0_2 · Cited by 438 · see citing works
On the Localizability of Quantum Mechanical Systems
Wightman, A. S. (1962) · Reviews of Modern Physics · doi:10.1103/revmodphys.34.845 · Cited by 417 · see citing works
(1996) · Progress in Optics · doi:10.1016/s0079-6638(08)70316-0 · Cited by 240 · see citing works
Photon wave functions, wave-packet quantization of light, and coherence theory
Smith, B. J., & Raymer, M. G. (2007) · New Journal of Physics · doi:10.1088/1367-2630/9/11/414 · Cited by 200 · see citing works
Note on Light Quanta and the Electromagnetic Field
Oppenheimer, J. R. (1931) · Physical Review · doi:10.1103/physrev.38.725 · Cited by 199 · see citing works
On the natures of the spin and orbital parts of optical angular momentum
Barnett, S. M., Allen, L., Cameron, R. P., Gilson, C. R., Padgett, M. J., Speirits, F. C., & Yao, A. M. (2016) · Journal of Optics · doi:10.1088/2040-8978/18/6/064004 · Cited by 182 · see citing works
Configuration Space Methods in Relativistic Quantum Field Theory. I
Wightman, A. S., & Schweber, S. S. (1955) · Physical Review · doi:10.1103/physrev.98.812 · Cited by 166 · see citing works
The Origin of Quantized Matter Waves
Darrigol, O. (1986) · Historical Studies in the Physical and Biological Sciences · doi:10.2307/27757565 · Cited by 136 · see citing works
Ingarden, R. S. (1976) · Reports on Mathematical Physics · doi:10.1016/0034-4877(76)90005-7 · Cited by 130 · see citing works
Mandeļ, L. (1963) · Progress in optics · doi:10.1016/s0079-6638(08)70560-2 · Cited by 118 · see citing works
The helicity of the free electromagnetic field and its physical meaning
Afanasiev, G. N., & Stepanovsky, Y. P. (1996) · Il Nuovo Cimento A · doi:10.1007/bf02731014 · Cited by 113 · see citing works
Exponential Localization of Photons
Białynicki‐Birula, I. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.5247 · Cited by 103 · see citing works
On the theory of spatial localization of photons
Keller, O. (2005) · Physics Reports · doi:10.1016/j.physrep.2005.01.002 · Cited by 99 · see citing works
Smith, B. J., & Raymer, M. G. (2006) · Physical Review A · doi:10.1103/physreva.74.062104 · Cited by 97 · see citing works
Pauli, W. E. F. (1980) · Springer eBooks · doi:10.1007/978-3-642-61840-6_10 · Cited by 84 · see citing works
BREIT, G. A. (1932) · Reviews of Modern Physics · doi:10.1103/revmodphys.4.504 · Cited by 71 · see citing works
Calculation of the Casimir energy at zero and finite temperature: Some recent resultsPreprint
Nesterenko, V. V., Lambiase, G., & SCARPETTA, G. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.hep-th/0503100 · Cited by 71 · see citing works
Barnett, S. M. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/9/093008 · Cited by 67 · see citing works
Białynicki‐Birula, I. (1996) · Springer eBooks · doi:10.1007/978-1-4757-9742-8_38 · Cited by 62 · see citing works
Photon wave functions in a localized coordinate space basis
Hawton, M. (1999) · Physical Review A · doi:10.1103/physreva.59.3223 · Cited by 55 · see citing works
Casimir energy of a compact cylinder under the condition ɛμ=c−2
Nesterenko, V. V., & Pirozhenko, I. G. (1999) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.60.125007 · Cited by 48 · see citing works
Multi-time wave functions for quantum field theory
Petrat, S., & Tumulka, R. (2014) · Annals of Physics · doi:10.1016/j.aop.2014.03.004 · Cited by 46 · see citing works
Why photons cannot be sharply localized
Białynicki‐Birula, I., & Białynicka-Birula, Z. (2009) · Physical Review A · doi:10.1103/physreva.79.032112 · Cited by 44 · see citing works
Space-time description of photon emission from an atom
Keller, O. (2000) · Physical Review A · doi:10.1103/physreva.62.022111 · Cited by 44 · see citing works
A Relativistic Schrödinger-like Equation for a Photon and Its Second Quantization
Kobe, D. H. (1999) · Foundations of Physics · doi:10.1023/a:1018855630724 · Cited by 42 · see citing works
Uncertainty Relation for Photons
Białynicki‐Birula, I., & Białynicka-Birula, Z. (2012) · Physical Review Letters · doi:10.1103/physrevlett.108.140401 · Cited by 41 · see citing works
Understanding interference experiments with polarized light through photon trajectories
Sanz, Á. S., Davidović, M., Božić, M., & Miret-Artés, S. (2010) · Annals of Physics · doi:10.1016/j.aop.2009.12.005 · Cited by 40 · see citing works
On the quantum-mechanics of a single photon
Kiessling, M. K. ‐., & Tahvildar-Zadeh, S. (2018) · Journal of Mathematical Physics · doi:10.1063/1.5021066 · Cited by 40 · see citing works
Photon wave mechanics and position eigenvectors
Hawton, M. (2007) · Physical Review A · doi:10.1103/physreva.75.062107 · Cited by 36 · see citing works
Boundary Conditions for the Description of Nuclear Reactions
Moshińsky, M. (1951) · Physical Review · doi:10.1103/physrev.81.347 · Cited by 35 · see citing works
Dual symmetric Lagrangians and conservation laws
Drummond, P. D. (1999) · Physical Review A · doi:10.1103/physreva.60.r3331 · Cited by 32 · see citing works
Quantum-mechanical description of optical beams
Bialynicki-Birula, I., & Bialynicka-Birula, Z. (2017) · Journal of Optics · doi:10.1088/2040-8986/aa98b6 · Cited by 32 · see citing works
On Rayleigh Scattering in Non-Relativistic Quantum Electrodynamics
Faupin, J., & Sigal, I. M. (2014) · Communications in Mathematical Physics · doi:10.1007/s00220-014-1883-6 · Cited by 29 · see citing works
Avoiding Ultraviolet Divergence by Means of Interior–Boundary Conditions
Teufel, S., & Tumulka, R. (2016) · Springer eBooks · doi:10.1007/978-3-319-26902-3_14 · Cited by 29 · see citing works
Particle Creation at a Point Source by Means of Interior-Boundary Conditions
Lampart, J., Schmidt, J., Teufel, S., & Tumulka, R. (2018) · Mathematical Physics Analysis and Geometry · doi:10.1007/s11040-018-9270-8 · Cited by 28 · see citing works
Electromagnetism as Quantum Physics
Sebens, C. T. (2019) · Foundations of Physics · doi:10.1007/s10701-019-00253-3 · Cited by 28 · see citing works
Maximal velocity of photons in non-relativistic QED
Bony, J., Faupin, J., & Sigal, I. M. (2012) · Advances in Mathematics · doi:10.1016/j.aim.2012.07.019 · Cited by 28 · see citing works
Lévy flights and nonlocal quantum dynamics
Garbaczewski, P., & Stephanovich, V. A. (2013) · Journal of Mathematical Physics · doi:10.1063/1.4814049 · Cited by 28 · see citing works
Dynamics of Charged Particles and their Radiation Field
Spohn, H. E. (2023) · Cambridge University Press eBooks · doi:10.1017/9781009402286 · Cited by 30 · see citing works
Babaei, H., & Mostafazadeh, A. (2017) · Journal of Mathematical Physics · doi:10.1063/1.4999847 · Cited by 25 · see citing works
Photon localization barrier can be overcome
Saari, P., Menert, M., & Valtna-Lukner, H. (2004) · Optics Communications · doi:10.1016/j.optcom.2004.11.020 · Cited by 25 · see citing works
Hamiltonians without ultraviolet divergence for quantum field theories
Teufel, S., & Tumulka, R. (2020) · Quantum Studies Mathematics and Foundations · doi:10.1007/s40509-020-00223-9 · Cited by 23 · see citing works
Quantization of Gauss–Hermite and Gauss–Laguerre beams in free space
Wünsche, A. (2004) · Journal of Optics B Quantum and Semiclassical Optics · doi:10.1088/1464-4266/6/3/009 · Cited by 23 · see citing works
Angular momentum and the geometrical gauge of localized photon states
Hawton, M., & Baylis, W. E. (2005) · Physical Review A · doi:10.1103/physreva.71.033816 · Cited by 22 · see citing works
Quantum cryptography and V A Kotel'nikov's one'time key and sampling theorems
Molotkov, S. N. (2006) · Uspekhi Fizicheskih Nauk · doi:10.3367/ufnr.0176.200607k.0777 · Cited by 21 · see citing works
Tumulka, R. (2018) · Entropy · doi:10.3390/e20060462 · Cited by 20 · see citing works
Strnad, J. (1981) · Physics Education · doi:10.1088/0031-9120/16/2/306 · Cited by 19 · see citing works
EXTENSION OF THE UNCERTAINTY PRINCIPLE TO RELATIVISTIC QUANTUM THEORY
(1965) · Elsevier eBooks · doi:10.1016/b978-0-08-010586-4.50011-0 · Cited by 18 · see citing works
La genèse du concept de champ quantique
Darrigol, O. (1984) · Annales de Physique · doi:10.1051/anphys:0198400903043300 · Cited by 18 · see citing works
Mathematical aspects of the quantum theory of fields parts I and II
Friedrichs, K. O. (1951) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160040202 · Cited by 18 · see citing works
Dual-symmetric Lagrangians in quantum electrodynamics: I. Conservation laws and multi-polar coupling
Drummond, P. D. (2006) · Journal of Physics B: Atomic, Molecular and Optical Physics · doi:10.1088/0953-4075/39/15/s06 · Cited by 16 · see citing works
Relativity and Chemical Bonding
Schwerdtfeger, P. (2014) · Wiley eBooks · doi:10.1002/9783527664696.ch11 · Cited by 17 · see citing works
Hodgson, D., Southall, J., Purdy, R., & Beige, A. (2022) · Frontiers in Photonics · doi:10.3389/fphot.2022.978855 · Cited by 15 · see citing works
Minimal Photon Velocity Bounds in Non-relativistic Quantum Electrodynamics
Faupin, J., & Sigal, I. M. (2013) · Journal of Statistical Physics · doi:10.1007/s10955-013-0862-1 · Cited by 14 · see citing works
Electrodynamics with magnetic monopoles: Photon wave mechanical theory
Keller, O. (2018) · Physical Review A · doi:10.1103/physreva.98.052112 · Cited by 10 · see citing works
Dirac equation for photons in a fibre: Origin of polarisation
Saito, S. (2024) · Heliyon · doi:10.1016/j.heliyon.2024.e28367 · Cited by 12 · see citing works
Stumpf, H. (1971) · Vieweg+Teubner eBooks · doi:10.1007/978-3-322-83700-4_13 · Cited by 10 · see citing works
<i>Zitterbewegung</i> of massless particles
Silenko, A. J. (2022) · Physical Review A · doi:10.1103/physreva.105.062211 · Cited by 11 · see citing works
“It is known that the photon and other massless particles cannot be spatially localized [15, 16, 43, 44].”
BackgroundNear-field photon wave mechanics in the Lorenz gauge
Keller, O. (2007) · Physical Review A · doi:10.1103/physreva.76.062110 · Cited by 9 · see citing works
Complete list of L D Landau's works
(1998) · Physics-Uspekhi · doi:10.1070/pu1998v041n06abeh000413 · Cited by 8 · see citing works
Interaction of a single-photon wave packet with an excited atom
Elyutin, P. V. (2012) · Physical Review A · doi:10.1103/physreva.85.033816 · Cited by 8 · see citing works
Hawton, M. (2010) · Physical Review A · doi:10.1103/physreva.82.012117 · Cited by 8 · see citing works
Interior-boundary conditions for Schrödinger operators on codimension-1 boundaries
Tumulka, R. (2020) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ab7ad2 · Cited by 7 · see citing works
Space-Time Probability Density of Detection of a Photon in Laser Beam of the Femtosecond Range
Davydov, A. P., & Zlydneva, T. P. (2018) · International Scientific-Technical Conference on Actual Problems of Electronic Instrument Engineering (APEIE) · doi:10.1109/apeie.2018.8545314 · Cited by 7 · see citing works
Davydov, A. P., & Zlydneva, T. P. (2020) · Journal of Physics Conference Series · doi:10.1088/1742-6596/1661/1/012028 · Cited by 7 · see citing works
Lill, S., Nickel, L., & Tumulka, R. (2021) · Annales Henri Poincaré · doi:10.1007/s00023-020-01009-w · Cited by 7 · see citing works
The Newton-Wigner and Wightman localization of the photon
Ingall, J. E. (1996) · Foundations of Physics · doi:10.1007/bf02061401 · Cited by 7 · see citing works
Zur Quantisierung nichtlinearer Gleichungen
Heisenberg, W. K. (1993) · Springer eBooks · doi:10.1007/978-3-642-70079-8_16 · Cited by 7 · see citing works
Note sur le formalisme des champs quantifies
Pirenne, J. (1949) · Physica · doi:10.1016/0031-8914(49)90065-8 · Cited by 7 · see citing works
On the Emergence of a Polychromatic Photon from a Single Atom
Keller, O. (2002) · Single Molecules · doi:10.1002/1438-5171(200204)3:1 · Cited by 7 · see citing works
On the wave-particle duality within the framework of modeling single-photon interference
Davydov, A. P., & Zlydneva, T. P. (2019) · Journal of Physics Conference Series · doi:10.1088/1742-6596/1399/2/022019 · Cited by 6 · see citing works
Chapter 3 Historical papers on the particle concept of light
Keller, O. (2007) · Progress in optics · doi:10.1016/s0079-6638(07)50003-x · Cited by 8 · see citing works
Redhead, M. L. G. (1977) · The British Journal for the Philosophy of Science · doi:10.1093/bjps/28.1.65 · Cited by 6 · see citing works
Davydov, A. P., & Zlydneva, T. P. (2016) · International Scientific-Technical Conference on Actual Problems of Electronic Instrument Engineering (APEIE) · doi:10.1109/apeie.2016.7806458 · Cited by 6 · see citing works
Limits for realizing single photons
Gulla, J., Ryen, K., & Skaar, J. (2023) · Physical Review A · doi:10.1103/physreva.108.063708 · Cited by 5 · see citing works
The Wigner-Newton state localization and the commutativity of the configuration space
Mir‐Kasimov, R. M. (2006) · Physics of Particles and Nuclei Letters · doi:10.1134/s1547477106050025 · Cited by 5 · see citing works
SU(N) symmetry of coherent photons controlled by rotated waveplates
Saito, S. (2024) · Heliyon · doi:10.48550/arxiv.2304.01216 · Cited by 5 · see citing works
Bertolotti, M., Bovino, F. A., & Sibilia, C. (2015) · Progress in optics · doi:10.1016/bs.po.2015.02.001 · Cited by 5 · see citing works
A new look at the position operator in quantum theory
Lev, F. M. (2015) · Physics of Particles and Nuclei · doi:10.1134/s1063779615010049 · Cited by 5 · see citing works
The Weyl – Wigner – Moyal Formalism on a Discrete Phase Space. II. The Photon Wigner Function
Przanowski, M., Tosiek, J., & Turrubiates, F. J. (2020) · Fortschritte der Physik · doi:10.1002/prop.202000061 · Cited by 5 · see citing works
Davydov, A. P., & Zlydneva, T. P. (2021) · International Scientific-Technical Conference on Actual Problems of Electronic Instrument Engineering (APEIE) · doi:10.1109/apeie52976.2021.9647611 · Cited by 5 · see citing works
Time-Symmetric Interactions and Quantum Electrodynamics
Krizan, J. E. (1970) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.1.2772 · Cited by 5 · see citing works
Davydov, A. P., & Zlydneva, T. P. (2020) · Journal of Physics Conference Series · doi:10.1088/1742-6596/1679/2/022051 · Cited by 4 · see citing works
Federico, M., & Jauslin, H. R. (2023) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/acd155 · Cited by 4 · see citing works
Davydov, A. P., & Zlydneva, T. P. (2022) · Lecture notes in networks and systems · doi:10.1007/978-3-030-97020-8_30 · Cited by 4 · see citing works
How small a packet of photons can be made?
Saari, P. (2006) · Laser Physics · doi:10.1134/s1054660x06040049 · Cited by 4 · see citing works
Møller, C. (1938) · Nature · doi:10.1038/142290b0 · Cited by 4 · see citing works
Quantum Theory over a Galois Field and Applications to Gravity and Particle TheoryPreprint
Lev, F. M. (2011) · arXiv (Cornell University) · Cited by 4 · see citing works
Wave-function equations for photons and electrons
Broyles, A. A. (1982) · Physical Review A · doi:10.1103/physreva.26.1181 · Cited by 4 · see citing works
Bosonization Method for Second Super Quantization
Dynin, A. (2010) · Journal of Nonlinear Mathematical Physics · doi:10.1142/s1402925110000763 · Cited by 4 · see citing works
Proof of the impossibility of a dynamical description of wave packet “reduction”
Lomsadze, Y. M., Kovalchuk, A. Y., & Krivsky, I. Y. (1965) · Physics Letters · doi:10.1016/0031-9163(65)91121-2 · Cited by 4 · see citing works
Drezet, A., & Nabet, B. M. (2026) · Symmetry · doi:10.3390/sym18010157 · Cited by 3 · see citing works
The Massless Limit of Bargmann–Wigner Equations for a Massive Graviton
Hradyskyi, A. V., & Stepanoskiy, Y. P. (2018) · Ukrainian Journal of Physics · doi:10.15407/ujpe63.7.584 · Cited by 3 · see citing works
On the photon–classical electromagnetic field relationship
Dragoman, D. (2025) · Annals of the New York Academy of Sciences · doi:10.1111/nyas.15378 · Cited by 3 · see citing works
Keller, O. (2006) · Laser and Particle Beams · doi:10.1017/s0263034606060113 · Cited by 3 · see citing works
Complete list of L D Landau's works
(1998) · Uspekhi Fizicheskih Nauk · doi:10.3367/ufnr.0168.199806l.0701 · Cited by 2 · see citing works
Nonlocality of the energy density for all single-photon states
Federico, M., & Jauslin, H. R. (2023) · Physical Review A · doi:10.1103/physreva.108.043720 · Cited by 2 · see citing works
Brainis, E., & Emplit, P. (2010) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.854265 · Cited by 2 · see citing works
On optical tunneling in near-field diffraction of light from a small hole
Jung, J., & Keller, O. (2017) · Journal of the Optical Society of America B · doi:10.1364/josab.34.000726 · Cited by 2 · see citing works
- Authors
- Landau, L., & Peierls, R.
- Venue
- Zeitschrift f�r Physik
- Published
- 1930-03
- Volume
- 62
- Issue
- 3-4
- Pages
- 188-200
- ISSN
- 1434-6001 (ISSN-L)
- 1434-601X
- OpenAlex
- W2017705068
- Cited by
- 150
- References
- 0
- Citations by year
- 2026: 5 · 2025: 5 · 2024: 7 · 2023: 9 · 2022: 3 · 2021: 4 · 2020: 6 · 2019: 4 · 2018: 6 · 2017: 4 · 2016: 5 · 2015: 2 · 2014: 7 · 2013: 2 · 2012: 5
- FWCI
- 3.18
- Type
- journal article
- Language
- de
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- The European Physical Journal A (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Strong Light-Matter Interactions
- Keywords
- quantum electrodynamics, configuration space, Schrödinger equation, photons, electromagnetic fields, field-matter interaction
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
