Moving Manifolds in Electromagnetic Fields

TL;DR

This paper develops dynamic non-linear equations describing the motion of surfaces in electromagnetic fields, unifying various physical models and applying the formalism to molecular and membrane dynamics.

Contribution

It introduces a novel set of equations for moving manifolds in electromagnetic fields derived from a minimal action principle, unifying multiple physical models.

Findings

Equations reduce to Maxwell, Euler, MHD, and Poisson-Boltzmann equations under different conditions.

Application to macro-molecules and membranes demonstrates the formalism's effectiveness.

Provides a new framework for analyzing dynamic surfaces in electromagnetic environments.

Abstract

We propose dynamic non-linear equations for moving surfaces in electromagnetic field. The field is induced by a material body with a boundary of the surface. Correspondingly the potential energy, set by the field at the boundary, can be written as an addition of four-potential times four-current to a contraction of electromagnetic tensor. Proper application of minimal action principle to the system Lagrangian yields dynamic non-linear equations for moving three dimensional manifolds in electromagnetic fields. The equations, in different conditions simplify to Maxwell equations for massless three surfaces, to Euler equations for dynamic fluid, to magneto-hydrodynamic equations and to Poisson-Boltzmann equation. To illustrate effectiveness of the equations of motion we apply the formalism to analyze dynamics of macro-molecules and membranes.