On the first quantization and quantum diversity of photons

authored by: Boris Chichkov
Abstract: Quantum theory of photons based on the first quantization technique, similar to that used by Schrödinger in the formulation of quantum mechanics, is considered. First, scalar quantum mechanics of photons operating with the photon wave functions is discussed. Using the first quantization, the wave equation, the Schrödinger-like equations, and the Dirac equation for photons are derived. Then, vector quantum mechanics of photons is introduced, which defines the electromagnetic vector fields. Using the first quantization, the Maxwell equations for photons in a magneto-dielectric medium are obtained. Because the photon's electric and magnetic fields satisfy the Maxwell equations, all that is known about the classical optical fields can be directly transferred to photons demonstrating their quantum diversity. Relationships between the scalar and vector quantum mechanics of photons and between the Dirac and Maxwell equations are analyzed. To describe the propagation of photons in dispersive media, modified Maxwell equations are introduced.
Organisation(s): Institute of Quantum Optics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines
QuantumFrontiers
Type: Article
Journal: Advanced Photonics
Volume: 7
ISSN: 2577-5421
Publication date: 18.08.2025
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Electronic, Optical and Magnetic Materials, Atomic and Molecular Physics, and Optics, Biomedical Engineering
Electronic version(s): https://doi.org/10.1117/1.AP.7.5.055001 (Access: Closed)

BibTeX

@article{445f9709f04144348646151fdf433b8f,
title = "On the first quantization and quantum diversity of photons",
abstract = "Quantum theory of photons based on the first quantization technique, similar to that used by Schr{\"o}dinger in the formulation of quantum mechanics, is considered. First, scalar quantum mechanics of photons operating with the photon wave functions is discussed. Using the first quantization, the wave equation, the Schr{\"o}dinger-like equations, and the Dirac equation for photons are derived. Then, vector quantum mechanics of photons is introduced, which defines the electromagnetic vector fields. Using the first quantization, the Maxwell equations for photons in a magneto-dielectric medium are obtained. Because the photon's electric and magnetic fields satisfy the Maxwell equations, all that is known about the classical optical fields can be directly transferred to photons demonstrating their quantum diversity. Relationships between the scalar and vector quantum mechanics of photons and between the Dirac and Maxwell equations are analyzed. To describe the propagation of photons in dispersive media, modified Maxwell equations are introduced.",
keywords = "dispersive media, first quantization, optics, photonics, photons, wave function",
author = "Boris Chichkov",
note = "Publisher Copyright: {\textcopyright} The Authors.",
year = "2025",
month = aug,
day = "18",
doi = "10.1117/1.AP.7.5.055001",
language = "English",
volume = "7",
journal = "Advanced Photonics",
issn = "2577-5421",
number = "5",
}