Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

CRC Press eBooks

The photon of the quantized electromagnetic field

Ole Keller

Published May 13, 2014• 0 citations
Publisher

Abstract

According to modern quantum field theory all elementary particles are quantum excitations of an underlying quantum field. In the case of the photon the underlying field is the electromagnetic field. In photon wave mechanics the photon concept was reached by a reinterpretation of the physical meaning of the free classical electromagnetic field. Such a reinterpretation does not give us a quantum theory of light quanta because the elementary quantum of action is foreign to classical physics. Although Planck’s constant does occur in the various Schro¨dinger-like wave equations we have presented in Part III it just plays the role of a multiplicative factor, see e.g., Eq. (10.36). The “justification” for bringing ~ into the formalism is the wish to make contact to the Einstein-de Broglie relations [Eqs. (10.40) and (10.41)]. In a sense one may call the light particle appearing from classical electrodynamics the classical photon.

DOI
10.1201/b16917-22

Related papers

A simple geometry-based model for the photon

Celso de Araújo Duarte

The classical and the quantum expressions of the energy of the electromagnetic radiation are compared. This comparison shows that, contrary to the commonly expected, the dependency of the energy [Formula: see text] of the photon with respect to the frequency [Formula: see text] on the Einstein–Planck relation [Formula: see text] is obtainable from classical electrodynamics, a fact that may provide a new historic perspective of the birth of quantum mechanics. It is suggested that the photon is a composite particle, constituted by quanta of electric and magnetic field fluxes maybe in an entangled state — being these two quanta either real or only as pseudo particles. It is also suggested a modification on the de Broglie’s fusion principle for the photon for the specific case in consideration.

arXiv:1305.3602•International Journal of Geometric Methods in Modern Physics•Jun 5, 2018•1 citation

Summarizing what we know about the photon

Harry Paul

How can we construct a picture of the photon from the wealth of observation material available to us? The photon appears to have a split personality: it is neither a wave nor a particle but something else which, depending on the experimental situation, exhibits a wave- or a particle-like behavior. In other words, in the photon (as in material particles such as the electron) the particle–wave dualism becomes manifest. Whereas classically the wave and the particle pictures are separate, quantum mechanics accomplishes a formal synthesis through a unified mathematical treatment. Let us look first at the wave aspect familiar from classical electrodynamics, which seems to be the most natural description. It makes all the different interference phenomena understandable, such as the “interference of the photon with itself” on the one hand and the appearance of spatial and temporal intensity correlations in a thermal radiation field on the other (which are obviously brought about by superposition of elementary waves emitted independently from different atoms). It might come as a surprise (at least for those having quantum mechanical preconceptions) that the classical theory is valid down to arbitrarily small intensities: the visibility of the interference pattern does not deteriorate even for very small intensities – the zero point fluctuations of the electromagnetic field advocated by quantum mechanics do not have a disturbing effect – and is valid not only for conventional interference experiments but also for interference between independently generated light beams (in the form of laser light).

Cambridge University Press eBooks•May 20, 2004•0 citations

From the Light Quantum to the Photon: The Evolution of a Physical Concept

Aaron Collavini, Valentina Bologna, Francesco Longo +2 more

This work examines the physical and conceptual evolution of the light quantum from Planck's blackbody theory to the theoretical and experimental developments that led to the quantization of the electromagnetic field. The present study shows that the decisive transition occurred in Einstein's quantum theory of radiation (1916-1917). Absorption, stimulated emission, and spontaneous emission were formulated as elementary probabilistic mechanisms whose statistical balance alone reproduces the blackbody spectrum. In particular, spontaneous emission requires the emission of a light quantum, thereby implicitly proving its physical necessity before its theoretical status was clarified. At the same time, the already existing term photon began to acquire a stable usage following Lewis's 1926 proposal and became increasingly associated with Einstein's light quantum. By the mid-1920s, the central problem had shifted from whether light quanta were physically required to how radiation could be incorporated into the emerging quantum-mechanical formalism. This transition marks a key stage, illustrating how initial debates about the existence of light quanta gave way to their integration into a comprehensive theoretical structure. The resulting asymmetry between the novel quantum description of matter and the still-classical description of radiation, called into question by the phenomenon of spontaneous emission, identifies the physical problem that led to the quantization of the electromagnetic field.

physics.hist-phCross-listedarXiv:2609.04985•Sep 7, 2026

The elusive light particle

Ole Keller

Classical electromagnetics in free space leaves no room for accommodation of a light particle. To underline this, it is sufficient to remember that Einstein in order to reach his lightquantum (energy-quantum) hypothesis had to mix classical theoretical physics with a piece of experimental information that defies description in classical terms. In his 1905-paper Einstein concluded [60]:Monochromatic radiation of low density (within the range of validity of Wien’s radiation formula) behaves thermodynamically as though it consisted of a number of mutually independent energy quanta of magnitude hν. The introduction of light quanta in the Wien regime (the high-frequency part of the Planck blackbody radiation law) is the first step toward the concept of electromagnetic radiation as a Bose gas of photons [180, 39, 68, 69]. Although a photon gas obeys Bose-Einstein statistics for all frequencies the statistical independence assumed by Einstein in 1905 is not true in general. Einstein used Boltzmann statistics when he conjectured the existence of light quanta. In the Wien regime Boltzmann and Bose-Einstein statistics lead to the same conclusion since the mean number of particles (photons) with a given energy is much less than one. The circumstance that the light quanta are not statistically independent in Bose-Einstein counting finds its explanation in quantum mechanics. Hence, the statistical correlation is induced by the requirement of totally symmetric wave functions.

CRC Press eBooks•May 13, 2014•0 citations

Quantum field theory of light

Ulf Leonhardt

Light in media The backbone of theoretical quantum optics is the quantum field theory of light, the quantum theory of the electromagnetic field. Quantum electrodynamics becomes surprisingly complicated if one insists on formulating it in a relativistically and gauge-invariant form, as one surely should do in elementary particle physics. Moreover, in quantum optics, we are concerned with light quanta in materials such as glass, with quantum electromagnetism in media, which is even more complicated. To cut a long story short, here we follow a minimalistic approach where we develop the essentials of quantum electrodynamics with as little technical effort as possible, sailing around the cliffs of relativistic quantum field theories. We do not assume any prior knowledge of classical field theory; we only borrow a few ideas from classical electromagnetism (Jackson, 1998). Complications and problems still remain, but hopefully these are mostly no longer formal difficulties, but rather conceptual problems of the quantum nature of light. As Dr Samuel Johnson said on poetry “We all know what light is; but it is not easy to tell what it is. ” Maxwell's equations What is light? Light is a quantum object - we describe its properties by quantum observables, Hermitian operators, and its state by a state vector | ψ _ or density matrix ρ . We use the Heisenberg picture of quantum mechanics where the operators evolve in time, but the quantum state does not change.

Cambridge University Press eBooks•Feb 18, 2010•0 citations

Quantum electrodynamics

Monique Combescot, Shiue-Yuan Shiau

Abstract In the chapter « Quantum electrodynamics », both the particles and the electromagnetic field are quantized. An elementary quantization procedure is first proposed in which the classical field normal modes are naïvely replaced by photon operators. The full quantization procedure is then presented that makes use of the Lagrangian formalism and the resulting Hamilton equations. This chapter ends with a discussion on photon number states and coherent Glauber states.

•Aug 5, 2026•0 citations
According to modern quantum field theory all elementary particles are quantum excitations of an underlying quantum field. In the case of the photon the underlying field is the electromagnetic field. In photon wave mechanics the photon concept was reached by a reinterpretation of the physical meaning of the free classical electromagnetic field. Such a reinterpretation does not give us a quantum theory of light quanta because the elementary quantum of action is foreign to classical physics. Although Planck’s constant does occur in the various Schro¨dinger-like wave equations we have presented in Part III it just plays the role of a multiplicative factor, see e.g., Eq. (10.36). The “justification” for bringing ~ into the formalism is the wish to make contact to the Einstein-de Broglie relations [Eqs. (10.40) and (10.41)]. In a sense one may call the light particle appearing from classical electrodynamics the classical photon.
The classical and the quantum expressions of the energy of the electromagnetic radiation are compared. This comparison shows that, contrary to the commonly expected, the dependency of the energy [Formula: see text] of the photon with respect to the frequency [Formula: see text] on the Einstein–Planck relation [Formula: see text] is obtainable from classical electrodynamics, a fact that may provide a new historic perspective of the birth of quantum mechanics. It is suggested that the photon is a composite particle, constituted by quanta of electric and magnetic field fluxes maybe in an entangled state — being these two quanta either real or only as pseudo particles. It is also suggested a modification on the de Broglie’s fusion principle for the photon for the specific case in consideration.
How can we construct a picture of the photon from the wealth of observation material available to us? The photon appears to have a split personality: it is neither a wave nor a particle but something else which, depending on the experimental situation, exhibits a wave- or a particle-like behavior. In other words, in the photon (as in material particles such as the electron) the particle–wave dualism becomes manifest. Whereas classically the wave and the particle pictures are separate, quantum mechanics accomplishes a formal synthesis through a unified mathematical treatment. Let us look first at the wave aspect familiar from classical electrodynamics, which seems to be the most natural description. It makes all the different interference phenomena understandable, such as the “interference of the photon with itself” on the one hand and the appearance of spatial and temporal intensity correlations in a thermal radiation field on the other (which are obviously brought about by superposition of elementary waves emitted independently from different atoms). It might come as a surprise (at least for those having quantum mechanical preconceptions) that the classical theory is valid down to arbitrarily small intensities: the visibility of the interference pattern does not deteriorate even for very small intensities – the zero point fluctuations of the electromagnetic field advocated by quantum mechanics do not have a disturbing effect – and is valid not only for conventional interference experiments but also for interference between independently generated light beams (in the form of laser light).
This work examines the physical and conceptual evolution of the light quantum from Planck's blackbody theory to the theoretical and experimental developments that led to the quantization of the electromagnetic field. The present study shows that the decisive transition occurred in Einstein's quantum theory of radiation (1916-1917). Absorption, stimulated emission, and spontaneous emission were formulated as elementary probabilistic mechanisms whose statistical balance alone reproduces the blackbody spectrum. In particular, spontaneous emission requires the emission of a light quantum, thereby implicitly proving its physical necessity before its theoretical status was clarified. At the same time, the already existing term photon began to acquire a stable usage following Lewis's 1926 proposal and became increasingly associated with Einstein's light quantum. By the mid-1920s, the central problem had shifted from whether light quanta were physically required to how radiation could be incorporated into the emerging quantum-mechanical formalism. This transition marks a key stage, illustrating how initial debates about the existence of light quanta gave way to their integration into a comprehensive theoretical structure. The resulting asymmetry between the novel quantum description of matter and the still-classical description of radiation, called into question by the phenomenon of spontaneous emission, identifies the physical problem that led to the quantization of the electromagnetic field.
Classical electromagnetics in free space leaves no room for accommodation of a light particle. To underline this, it is sufficient to remember that Einstein in order to reach his lightquantum (energy-quantum) hypothesis had to mix classical theoretical physics with a piece of experimental information that defies description in classical terms. In his 1905-paper Einstein concluded [60]:Monochromatic radiation of low density (within the range of validity of Wien’s radiation formula) behaves thermodynamically as though it consisted of a number of mutually independent energy quanta of magnitude hν. The introduction of light quanta in the Wien regime (the high-frequency part of the Planck blackbody radiation law) is the first step toward the concept of electromagnetic radiation as a Bose gas of photons [180, 39, 68, 69]. Although a photon gas obeys Bose-Einstein statistics for all frequencies the statistical independence assumed by Einstein in 1905 is not true in general. Einstein used Boltzmann statistics when he conjectured the existence of light quanta. In the Wien regime Boltzmann and Bose-Einstein statistics lead to the same conclusion since the mean number of particles (photons) with a given energy is much less than one. The circumstance that the light quanta are not statistically independent in Bose-Einstein counting finds its explanation in quantum mechanics. Hence, the statistical correlation is induced by the requirement of totally symmetric wave functions.
Light in media The backbone of theoretical quantum optics is the quantum field theory of light, the quantum theory of the electromagnetic field. Quantum electrodynamics becomes surprisingly complicated if one insists on formulating it in a relativistically and gauge-invariant form, as one surely should do in elementary particle physics. Moreover, in quantum optics, we are concerned with light quanta in materials such as glass, with quantum electromagnetism in media, which is even more complicated. To cut a long story short, here we follow a minimalistic approach where we develop the essentials of quantum electrodynamics with as little technical effort as possible, sailing around the cliffs of relativistic quantum field theories. We do not assume any prior knowledge of classical field theory; we only borrow a few ideas from classical electromagnetism (Jackson, 1998). Complications and problems still remain, but hopefully these are mostly no longer formal difficulties, but rather conceptual problems of the quantum nature of light. As Dr Samuel Johnson said on poetry “We all know what light is; but it is not easy to tell what it is. ” Maxwell's equations What is light? Light is a quantum object - we describe its properties by quantum observables, Hermitian operators, and its state by a state vector | ψ _ or density matrix ρ . We use the Heisenberg picture of quantum mechanics where the operators evolve in time, but the quantum state does not change.