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Cited by 240Quantum and Classical ElectrodynamicsQuantum Mechanics and ApplicationsRelativity and Gravitational Theory

V Photon Wave Function

Open access
Iwo Białynicki‐Birula·1996·Progress in Optics
DOI 10.1016/s0079-6638(08)70316-0
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Abstract

This chapter describes the photon wave function, and explains the basic properties of a well-defined mathematical object—a six-component function of space-time variables—that describes the quantum state of the photon. The most essential property that does not hold for the photon wave function is that the argument of the wave function cannot be directly associated with the position operator of the photon. The position operator for the photon simply does not exist. However, one should remember that for massive particles also, the true position operator exists only in the nonrelativistic approximation. The concept of localization associated with the Newton-Wigner position operator is not relativistically invariant. The photon wave function is not restricted to the wave mechanics of photons. The same wave functions also appear as mode functions in the expansion of the electromagnetic field operators.

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Crossref · 10.1016/s0079-6638(08)70316-0

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  • The difference in form for the helicity operator in the optical Dirac equation compared with the electron is not surprising because it has been true for each mechanical property considered, originating in the fact that ψ†ψ has dimensions of probability density for the electron but energy density for the electromagnetic field.

    “The difference in form for the helicity operator in the optical Dirac when compared with the analogous quantity for the electron should not come as a surprise, as this has been true for each of the mechanical properties we have considered and has its origins in the fact that ψ ψ † has the dimensions of a probability density for the electron but an energy density for the electromagnetic fi eld [16]”

    From Optical Dirac equation (2014) · cites this paper as [16]

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  • The method of relativistic FW transformation is applicable for a particle in arbitrarily strong external fields, without taking into account effects of quantum field theory.

    “It is applicable for a particle in arbitrarily strong external fields (without taking into account effects of quantum field theory).”

    From <i>Zitterbewegung</i> of massless particles (2022) · cites this paper as [87]

    The passages on relativistic photon wave mechanics (§7) and transformation properties (§3.2) discuss Poincaré and Lorentz transformations, not the Foldy–Wouthuysen (FW) method. Searches for FW transformation, arbitrarily strong external fields, and the exclusion of quantum-field-theory effects found no passage addressing the claimed applicability. (LLM, conf=0.76)

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  • The FW transformation method gives exact and compact relativistic expressions for all terms proportional to the zero and first powers of the Planck constant and only for such terms proportional to hbar^2 which describe contact interactions, including the Darwin one.

    “However, the FW transformation method [42,44,63,87] applied also in Ref. [27] gives exact and compact relativistic expressions for all terms proportional to the zero and first powers of the Planck constant and only for such terms proportional to ¯ h 2 which describe contact interactions (including the Darwin one).”

    From <i>Zitterbewegung</i> of massless particles (2022) · cites this paper as [87]

    Split into 2 atoms — 0 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 2 unverifiable. Expand the claim to see per-atom verdicts.

    Experimental — accuracy not yet measured

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Cites

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3 of the 96 references couldn’t be matched to a known paper.

Research works printed but not linked: 2

  1. Bateman, H., 1915, The Mathematical Analysis of Electrical and Optical Wave Motion on the Basis of Maxwell's Equations (Cambridge). Reprinted: 1955 (Dover, New York).
  2. hydrogenic atoms, Phys. Rev. A 8, 1710. 400. the quantum theory of elementary particles, Proc. R. SOC. (London) A 195, 62. p. 995.

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Authors
Białynicki‐Birula, I.
Affiliations
Center for Theoretical Physics (PL)
Corresponding author
Iwo Białynicki‐Birula
ORCID
Iwo Białynicki‐Birula
Venue
Progress in Optics
Publisher
Elsevier
Published
1996
Pages
245-294
ISSN
0079-6638 (ISSN-L)
DOI
10.1016/s0079-6638(08)70316-0
OpenAlex
W1968483883
Cited by
240
References
96
Citations by year
2026: 8 · 2025: 18 · 2024: 16 · 2023: 17 · 2022: 9 · 2021: 23 · 2020: 10 · 2019: 14 · 2018: 11 · 2017: 15 · 2016: 11 · 2015: 13 · 2014: 5 · 2013: 7 · 2012: 9
FWCI
5.51
Type
book chapter
Language
en
Open access
Licence
Locations
Progress in optics (publishedVersion, cc-by-nc-nd)
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 › Astronomy and Astrophysics › Relativity and Gravitational Theory
Keywords
photon wave function, position operator, localization, relativistic invariance, mode functions

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