Electrodynamics of Perfect Conductors

TL;DR

This paper derives the fundamental electrodynamic equations governing perfect conductors using variational principles, showing that magnetic field expulsion results from zero resistivity rather than superconductivity.

Contribution

It presents a unified derivation of perfect conductor electrodynamics from classical and quantum perspectives, clarifying the origin of magnetic field expulsion.

Findings

London equations as a special case of the derived equations

Magnetic field expulsion linked to zero resistivity, not superconductivity

Consistent derivation from classical and quantum models

Abstract

The most general electrodynamic equations of a perfect conducting state are obtained using a variational principle in a classical framework, following an approach by Pierre-Gilles de Gennes. London equations are derived as the time-independent case of these equations, corresponding to the magnetostatic minimal energy state of the perfect conducting system. For further confirmation, the same equations are also derived in the classical limit of the Coleman-Weinberg model, the most successful quantum macroscopic theory of superconductivity. The magnetic field expulsion is, therefore, a direct consequence of zero resistivity and not an exclusive property of superconductors.