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V Photon Wave Function
Open accessAbstract
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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“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]”
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“It is applicable for a particle in arbitrarily strong external fields (without taking into account effects of quantum field theory).”
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“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).”
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Born, M., Wolf, E., Bhatia, A. B., Clemmow, P. C., Gabor, D., Stokes, A. R., Taylor, A. M., Wayman, P. A., & Wilcock, W. L. (1999) · Cambridge University Press eBooks · doi:10.1017/9781108769914 · Cited by 26,627
(2020) · Princeton University Press eBooks · doi:10.2307/j.ctv131bv37.5 · Cited by 22,595
Messiah, A. (1961) · Cited by 16,012
On the Quantum Correction For Thermodynamic Equilibrium
Wigner, E. (1932) · Physical Review · doi:10.1103/physrev.40.749 · Cited by 9,283
Optical Coherence and Quantum Optics
Mandel, L., & Wolf, E. (1995) · doi:10.1017/cbo9781139644105 · Cited by 8,356
Itzykson, C., & Zuber, J.-B. (1980) · Cited by 5,652
Weinberg, S. (1996) · Cambridge University Press eBooks · doi:10.1017/cbo9781139644174 · Cited by 4,420
Schwartz, M. D. (2013) · Cambridge University Press eBooks · doi:10.1017/9781139540940.014 · Cited by 3,375
On Unitary Representations of the Inhomogeneous Lorentz Group
Wigner, E. P. (1939) · Annals of Mathematics · doi:10.2307/1968551 · Cited by 3,113
Schiff, L. I. (1949) · Cited by 3,018
Research works printed but not linked: 1
- Skrotski, 1957, The influence of gravitation on the propagation of light, Sov. Phys. Dokl., 2, 226
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Metadata
- Authors
- Białynicki‐Birula, I.
- Affiliations
- Center for Theoretical Physics (PL)
- Corresponding author
- Iwo Białynicki‐Birula
- Venue
- Progress in Optics
- Publisher
- Elsevier
- Published
- 1996
- Pages
- 245-294
- ISSN
- 0079-6638 (ISSN-L)
- 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
- hybrid
- doi.org
- 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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