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

arXiv:1004.4316

Quantum form of Nonlinear Maxwell Equation

Y. Chen, Zhang, F. L., J.L. Chen

Published Apr 25, 2010• 0 citations
arXivHTMLPDF

Abstract

We generalize Maxwell equations which describe the vacuum of quantum electrodynamics into the quantum form. This nontraditional approach is different from the widely used theory|-Quantum Electrodynamics. From another viewpoint, it could be a direction for interpreting quantum theories properly.
DOI
10.48550/arxiv.1004.4316

Related papers

On classical electrodynamics in Dirac's equation matrix form

Alexander G. Kyriakos

In the present paper it is shown that the Maxwell theory can be finely represented in the matrix form of Dirac's equation, if the Dirac wave function is identified with the electromagnetic wave by defined way. It seems to us, that such representation allows us to see new possibilities in the connection of the classical and quantum electrodynamics.

arXiv:quant-ph/0301151•Jan 27, 2003•0 citations

Quantum electrodynamics of equilibrium systems: A rigorous Maxwell-regularized functional-theoretic formulation

Markus Penz, Christian Jöns, Michael Ruggenthaler +1 more

A framework for quantum electrodynamics of equilibrium systems is proposed that takes the Maxwell equations as foundational and links them to the structure of density-functional theory for the quantum system. By switching from purely internal observables like the one-particle density to combined internal and external quantities, the external sources and their energy are taken into account. A fully regularized functional theory emerges that avoids the usual representability problems. With the Kohn-Sham construction that links to an auxiliary uncoupled system, the ultra-violet cutoff can be removed and one arrives at a fully renormalized and non-perturbative light-matter description. Regularized forms of density-functional theory with and without magnetic fields appear as boundary cases, while the emergent physical picture reproduces the macroscopic Maxwell equations.

cond-mat.mtrl-sciCross-listedarXiv:2609.18327•Sep 17, 2026

Maxwell's equations and quantum mechanics

Alojz Suhadolnik, Tilen Suhadolnik, Aljaž Suhadolnik

The free electron is undoubtedly an electromagnetic particle. However, the fundamental equations describing the free electron in quantum mechanics do not account for its electromagnetic properties; instead, they are based solely on its mechanical characteristics. Such treatment is insufficient for a complete description. In conventional quantum mechanics, the free-electron Schrödinger equation remains unrelated to Maxwell's differential equations. By considering the electron as both a quantum mechanical oscillator and a quantum electrodynamic oscillator, it becomes possible to derive the free-electron Schrödinger equation directly from Maxwell's equations. This article presents a novel theoretical approach to treating the electron, providing a simple and transparent derivation that, to the best of our knowledge, has not yet been published in the literature.

Physics Essays•Dec 10, 2025•0 citations

Derivation of general Maxwell type equations for open quantum systems

A. V. Khugaev, Gurgen Grigorievich Adamian, N. V. Antonenko

Using equations of motion with the anisotropic dissipative term for quantum particle and quantum-mechanical commutation rules, the general Maxwell-type differential equations are derived. The direct modifications of the well-known Maxwell equations due to the medium effects (openness of the system) are discussed.

arXiv:1901.04332•Jan 11, 2019•0 citations

Generalized theory of nonlinear quantum optics

M. Babiker

A quantum theory of nonlinear phenomena is considered in which account is taken of all contributions from electric and magnetic multipoles, without any multipolar approximation. Exact closed analytical expressions for the multipoles are first obtained from quantum electrodynamics by applying a generalization of the Power-Zienau transformation. The standard procedure is invoked to calculate general electromagnetic susceptibility tensors ${\ensuremath{\chi}}_{\ensuremath{\mu}\ensuremath{\nu}{\ensuremath{\alpha}}_{1}{\ensuremath{\beta}}_{1}\ensuremath{\cdots}{\ensuremath{\alpha}}_{n}{\ensuremath{\beta}}_{n}}^{[n]}$ (${\ensuremath{\omega}}_{1}, \dots{}, {\ensuremath{\omega}}_{n}$). Such a tensor is a shorthand for the electric and magnetic susceptibilities as well as mixed susceptibilities. By considering a relativistic theory based on the Dirac equation, the spin susceptibilities are automatically included. The formalism in this way allows for the computation of a wide range of electro- and magneto-optical effects to any order of perturbation and to any order of multipolar approximation.

Physical Review A•Jan 1, 1975•8 citations

Quantum Theory in the Electrical Engineering Curriculum

Dale M. Grimes

An approach to quantum theory tailored for those students whose backgrounds include relative strength in classical electromagnetic field theory but less in classical mechanics is described. Rather than building quantum theory by following the historical steps, as is often done, the technique is to approach the subject directly from a background knowledge of electromagnetic field theory. The approach uses the postulates that the Maxwell equations are always valid for point charges, that a form of steady-state cosmology is correct, and that the superposition principle is applicable to statistical processes. The model permits a direct transition from electromagnetic field theory to quantum theory. It is self-consistent and based upon currently acceptable physical postulates. It meets the epistemological objections against the orthodox interpretation that Einstein raised and that have never been adequately answered. It does not fall into the class of proposed interpretations that Wigner showed to be inconsistent with the wave theory.

IEEE Transactions on Education•Jun 1, 1965•2 citations
A framework for quantum electrodynamics of equilibrium systems is proposed that takes the Maxwell equations as foundational and links them to the structure of density-functional theory for the quantum system. By switching from purely internal observables like the one-particle density to combined internal and external quantities, the external sources and their energy are taken into account. A fully regularized functional theory emerges that avoids the usual representability problems. With the Kohn-Sham construction that links to an auxiliary uncoupled system, the ultra-violet cutoff can be removed and one arrives at a fully renormalized and non-perturbative light-matter description. Regularized forms of density-functional theory with and without magnetic fields appear as boundary cases, while the emergent physical picture reproduces the macroscopic Maxwell equations.
The free electron is undoubtedly an electromagnetic particle. However, the fundamental equations describing the free electron in quantum mechanics do not account for its electromagnetic properties; instead, they are based solely on its mechanical characteristics. Such treatment is insufficient for a complete description. In conventional quantum mechanics, the free-electron Schrödinger equation remains unrelated to Maxwell's differential equations. By considering the electron as both a quantum mechanical oscillator and a quantum electrodynamic oscillator, it becomes possible to derive the free-electron Schrödinger equation directly from Maxwell's equations. This article presents a novel theoretical approach to treating the electron, providing a simple and transparent derivation that, to the best of our knowledge, has not yet been published in the literature.
A quantum theory of nonlinear phenomena is considered in which account is taken of all contributions from electric and magnetic multipoles, without any multipolar approximation. Exact closed analytical expressions for the multipoles are first obtained from quantum electrodynamics by applying a generalization of the Power-Zienau transformation. The standard procedure is invoked to calculate general electromagnetic susceptibility tensors ${\ensuremath{\chi}}_{\ensuremath{\mu}\ensuremath{\nu}{\ensuremath{\alpha}}_{1}{\ensuremath{\beta}}_{1}\ensuremath{\cdots}{\ensuremath{\alpha}}_{n}{\ensuremath{\beta}}_{n}}^{[n]}$ (${\ensuremath{\omega}}_{1}, \dots{}, {\ensuremath{\omega}}_{n}$). Such a tensor is a shorthand for the electric and magnetic susceptibilities as well as mixed susceptibilities. By considering a relativistic theory based on the Dirac equation, the spin susceptibilities are automatically included. The formalism in this way allows for the computation of a wide range of electro- and magneto-optical effects to any order of perturbation and to any order of multipolar approximation.
An approach to quantum theory tailored for those students whose backgrounds include relative strength in classical electromagnetic field theory but less in classical mechanics is described. Rather than building quantum theory by following the historical steps, as is often done, the technique is to approach the subject directly from a background knowledge of electromagnetic field theory. The approach uses the postulates that the Maxwell equations are always valid for point charges, that a form of steady-state cosmology is correct, and that the superposition principle is applicable to statistical processes. The model permits a direct transition from electromagnetic field theory to quantum theory. It is self-consistent and based upon currently acceptable physical postulates. It meets the epistemological objections against the orthodox interpretation that Einstein raised and that have never been adequately answered. It does not fall into the class of proposed interpretations that Wigner showed to be inconsistent with the wave theory.