Feynman’s proof of the Maxwell equations

Comment on “Feynman’s Proof of the Maxwell Equations”

From Feynman Proof of Maxwell Equations to Noncommutative Quantum Mechanics

In 1990, Dyson published a proof due to Feynman of the Maxwell equations assuming only the commutation relations between position and velocity. With this minimal assumption, Feynman never supposed the existence of Hamiltonian or Lagrangian formalism. In the present communication, we review the study of a relativistic particle using “Feynman brackets.” We show that Poincaré’s magnetic angular mo...

The Stationary Maxwell-dirac Equations

The Maxwell-Dirac equations are the equations for electronic matter, the “classical” theory underlying QED. The system combines the Dirac equations with the Maxwell equations sourced by the Dirac current. A stationary Maxwell-Dirac system has ψ = eφ, with φ independent of t. The system is said to be isolated if the independent variables obey quite weak regularity and decay conditions. In this p...

1 The exact proof that Maxwell equations with the 3D E

In this paper it will be exactly proved both in the geometric algebra and tensor formalisms that the usual Maxwell equations with the three-dimensional (3D) vectors of the electric and magnetic fields, E and B respectively, are not, contrary to the general opinion, Lorentz covariant equations. Consequently they are not equivalent to the field equations with the observer independent quantities, ...

Compressible Euler-Maxwell Equations

The Euler-Maxwell equations as a hydrodynamic model of charge transport of semiconductors in an electromagnetic field are studied. The global approximate solutions to the initial-boundary value problem are constructed by the fractional Godunov scheme. The uniform bound and H−1 compactness are proved. The approximate solutions are shown convergent by weak convergence methods. Then, with some new...