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

AIP conference proceedings

A New Comment on Dyson’s Exposition of Feynman’s Proof of Maxwell Equations

Claudia Pombo, Luigi Accardi, Guillaume Adenier, Christopher A. Fuchs, Gregg S. Jaeger, Andrei Yu. Khrennikov, Jan-Åke Larsson, Stig Stenholm

Published Jan 1, 2009• 3 citations
Publisher

Abstract

A paper by Dyson, published nearly two decades ago, describing Feynman’s proof of Maxwell equations, has generated many comments, analysis, discussions and generalizations of the proof. Feynman’s derivation is assumed to be based on two main sets of equations. One is supposed to be the second law of Newton and the other a set of basic commutation relations from quantum physics.Here we present a new comment on this paper, focusing mainly on the initial arguments and applying a new method of analysis and interpretation of physics, named observational realism. The present discussion does not alter the technical steps of Feynman, but do clarify their basis. We show that Newton’s physics is not a starting point in Feynman’s derivation, neither is quantum physics involved in it, but the foundations of relativity only.

DOI
10.1063/1.3109963

Related papers

Time evolutions in Quantum mechanics and (Lorentzian) geometry

Paschke, Mario

As R.Feynman has shown to F. Dyson -- who published it then in 1990 under the name of "Feynman's proof of Maxwell's equations" -- the only interactions compatible with the canonical uncertainty relation (for scalar particles on flat $\R^3$) are the Lorentz covariant electromagnetic interactions. We generalize Feynman's argument to arbitrary configuration spaces, thereby clarifying its hidden assumptions as well as its geometrical significance. In addition, our result establishes a correspondence between globally hyperbolic spacetimes and solutions to our (algebraically formulated) axioms for nonrelativistic quantum mechanics.

arXiv:math-ph/0301040•Jan 29, 2003•2 citations

NONCOMMUTATIVE QUANTUM MECHANICS VIEWED FROM FEYNMAN FORMALISM

José Lages, Alain Bérard, Hervé Mohrbach +2 more

Dyson published in 1990 a proof due to Feynman of the Maxwell equations. This proof is based on the assumption of simple commutation relations between position and velocity. We first study a nonrelativistic particle using Feynman formalism. We show that Poincaré's magnetic angular momentum and Dirac magnetic monopole are the direct consequences of the structure of the sO(3) Lie algebra in Feynman formalism. Then we show how to extend this formalism to the dual momentum space with the aim of introducing Noncommutative Quantum Mechanics which was recently the subject of a wide range of works from particle physics to condensed matter physics.

arXiv:0709.0816•Beyond the Quantum•Sep 1, 2007•2 citations

NONCOMMUTATIVE QUANTUM MECHANICS VIEWED FROM FEYNMAN FORMALISM

José Lages, Alain Bérard, Hervé Mohrbach +2 more

Dyson published in 1990 a proof due to Feynman of the Maxwell equations. This proof is based on the assumption of simple commutation relations between position and velocity. We first study a nonrelativistic particle using Feynman formalism. We show that Poincar\'{e}'s magnetic angular momentum and Dirac magnetic monopole are the direct consequences of the structure of the sO(3) Lie algebra in Feynman formalism. Then we show how to extend this formalism to the dual momentum space with the aim of introducing Noncommutative Quantum Mechanics which was recently the subject of a wide range of works from particle physics to condensed matter physics.

•Jan 1, 2007•0 citations

Some Comments on the Foundations of Physics

Per‐Olov Löwdin

This pedagogical monograph describes some of the fundamental views of the laws of physics. The derivations are, however, obtained from a rather unconventional point of view. The Lorentz transformations and the special theory of relativity are derived without mentioning the phenomenon of light, and the de Broglie relations in the wave-corpuscle parallelism are derived without the help of Planck's constant. By the use of Schrodinger's idea of quantization as an eigenvalue problem, the foundations of wave mechanics are discussed as a mathematical problem without reference to Planck's constant. Finally, the Kepler problem in the special theory of relativity is studied starting from the energy law, and the applications to the Hulse-Taylor binary pulsar indicate that more data about the unseen companion are needed before the interpretation of the present data may be taken as the ultimate proof of the validity of the general theory of relativity.

WORLD SCIENTIFIC eBooks•Jan 1, 1998•5 citations

Quantum Maxwell's Equations Made Simple: Employing Scalar and Vector Potential Formulation

Weng Cho Chew, Dong-Yeop Na, Peter A. Bermel +3 more

We present a succinct way to quantize Maxwell's equations. We begin by discussing the random nature of quantum observables. Then we present the quantum Maxwell's equations and give their physical meanings. Due to the mathematical homomorphism between the classical and quantum cases [1], the derivation of quantum Maxwell's equations can be simplified. First, one needs only to verify that the classical equations of motion are derivable from a Hamiltonian by energy-conservation arguments. Then the quantum equations of motion follow due to homomorphism, which applies to sum-separable Hamiltonians. Hence, we first show the derivation of classical Maxwell's equations using Hamiltonian theory. Then the derivation of the quantum Maxwell's equations follows in an analogous fashion. Finally, we apply this quantization procedure to the dispersive medium case. (This article is written for the classical electromagnetic community assuming little knowledge of quantum theory, an introduction of which can be found in [2, Lecs. 38 and 39].)

IEEE Antennas and Propagation Magazine•Dec 9, 2020•30 citations

HUYGENS' PRINCIPLE, PHYSICS AND COMPUTERS

KEITH BOWDEN

We discuss the emergence of topology from a consideration of set extensions in General Systems Theory. Boundaries arise in a natural way, separating independent elements or regions of the system. Our aim is a unification of Etter theory, Kron's method of Tearing and Jessel's formulation of Huygens' Principle. This should make explicit the equivalence between the objective, structural, holographic and the subjective, relative definitions of information, sought in Bowden (1994b), reprinted in this Special Issue. It connects the abstract generalisations of Schrodinger's equation and Bom's rule derived in probabilistic Etter theory with the real world of electrical and other physical phenomena in General Physical Systems Theory. This paper can be considered as a continuation of Bowden (1990; 1994a) and as a response to Bowden (1994b), reprinted in this issue. We review the ideas behind Kron's Method of Tearing and Jessel's Principle of Secondary sources (both special cases of the above theory) and their equivalence. We follow Hiley's argument in Hiley (1996) to show how Schrodinger's equation can be thought of as specifying the evolution of (a series of) tearings in continuous space. These can be shown on a commutative diagram as a series of similarity transforms. We compare this with Etter's derivation (Etter, 1998). We describe briefly a recently published derivation of Maxwell's equations from a non-commutative algebra and show how they fit onto a related commutative diagram. Finally we make some comments on applications of the general theory to computer systems. This paper is a series of vignettes of work in progress. It is designed to point the direction of work to come in Constructive Physics.

International Journal of General Systems•Nov 1, 1998•1 citation
A paper by Dyson, published nearly two decades ago, describing Feynman’s proof of Maxwell equations, has generated many comments, analysis, discussions and generalizations of the proof. Feynman’s derivation is assumed to be based on two main sets of equations. One is supposed to be the second law of Newton and the other a set of basic commutation relations from quantum physics.Here we present a new comment on this paper, focusing mainly on the initial arguments and applying a new method of analysis and interpretation of physics, named observational realism. The present discussion does not alter the technical steps of Feynman, but do clarify their basis. We show that Newton’s physics is not a starting point in Feynman’s derivation, neither is quantum physics involved in it, but the foundations of relativity only.
As R.Feynman has shown to F. Dyson -- who published it then in 1990 under the name of "Feynman's proof of Maxwell's equations" -- the only interactions compatible with the canonical uncertainty relation (for scalar particles on flat R3\R^3R3) are the Lorentz covariant electromagnetic interactions. We generalize Feynman's argument to arbitrary configuration spaces, thereby clarifying its hidden assumptions as well as its geometrical significance. In addition, our result establishes a correspondence between globally hyperbolic spacetimes and solutions to our (algebraically formulated) axioms for nonrelativistic quantum mechanics.
Dyson published in 1990 a proof due to Feynman of the Maxwell equations. This proof is based on the assumption of simple commutation relations between position and velocity. We first study a nonrelativistic particle using Feynman formalism. We show that Poincaré's magnetic angular momentum and Dirac magnetic monopole are the direct consequences of the structure of the sO(3) Lie algebra in Feynman formalism. Then we show how to extend this formalism to the dual momentum space with the aim of introducing Noncommutative Quantum Mechanics which was recently the subject of a wide range of works from particle physics to condensed matter physics.
Dyson published in 1990 a proof due to Feynman of the Maxwell equations. This proof is based on the assumption of simple commutation relations between position and velocity. We first study a nonrelativistic particle using Feynman formalism. We show that Poincar\'{e}'s magnetic angular momentum and Dirac magnetic monopole are the direct consequences of the structure of the sO(3) Lie algebra in Feynman formalism. Then we show how to extend this formalism to the dual momentum space with the aim of introducing Noncommutative Quantum Mechanics which was recently the subject of a wide range of works from particle physics to condensed matter physics.
This pedagogical monograph describes some of the fundamental views of the laws of physics. The derivations are, however, obtained from a rather unconventional point of view. The Lorentz transformations and the special theory of relativity are derived without mentioning the phenomenon of light, and the de Broglie relations in the wave-corpuscle parallelism are derived without the help of Planck's constant. By the use of Schrodinger's idea of quantization as an eigenvalue problem, the foundations of wave mechanics are discussed as a mathematical problem without reference to Planck's constant. Finally, the Kepler problem in the special theory of relativity is studied starting from the energy law, and the applications to the Hulse-Taylor binary pulsar indicate that more data about the unseen companion are needed before the interpretation of the present data may be taken as the ultimate proof of the validity of the general theory of relativity.
We present a succinct way to quantize Maxwell's equations. We begin by discussing the random nature of quantum observables. Then we present the quantum Maxwell's equations and give their physical meanings. Due to the mathematical homomorphism between the classical and quantum cases [1], the derivation of quantum Maxwell's equations can be simplified. First, one needs only to verify that the classical equations of motion are derivable from a Hamiltonian by energy-conservation arguments. Then the quantum equations of motion follow due to homomorphism, which applies to sum-separable Hamiltonians. Hence, we first show the derivation of classical Maxwell's equations using Hamiltonian theory. Then the derivation of the quantum Maxwell's equations follows in an analogous fashion. Finally, we apply this quantization procedure to the dispersive medium case. (This article is written for the classical electromagnetic community assuming little knowledge of quantum theory, an introduction of which can be found in [2, Lecs. 38 and 39].)
We discuss the emergence of topology from a consideration of set extensions in General Systems Theory. Boundaries arise in a natural way, separating independent elements or regions of the system. Our aim is a unification of Etter theory, Kron's method of Tearing and Jessel's formulation of Huygens' Principle. This should make explicit the equivalence between the objective, structural, holographic and the subjective, relative definitions of information, sought in Bowden (1994b), reprinted in this Special Issue. It connects the abstract generalisations of Schrodinger's equation and Bom's rule derived in probabilistic Etter theory with the real world of electrical and other physical phenomena in General Physical Systems Theory. This paper can be considered as a continuation of Bowden (1990; 1994a) and as a response to Bowden (1994b), reprinted in this issue. We review the ideas behind Kron's Method of Tearing and Jessel's Principle of Secondary sources (both special cases of the above theory) and their equivalence. We follow Hiley's argument in Hiley (1996) to show how Schrodinger's equation can be thought of as specifying the evolution of (a series of) tearings in continuous space. These can be shown on a commutative diagram as a series of similarity transforms. We compare this with Etter's derivation (Etter, 1998). We describe briefly a recently published derivation of Maxwell's equations from a non-commutative algebra and show how they fit onto a related commutative diagram. Finally we make some comments on applications of the general theory to computer systems. This paper is a series of vignettes of work in progress. It is designed to point the direction of work to come in Constructive Physics.