Electromagnetism from relativistic fluid dynamics

Abstract

We reformulate classical electromagnetism within the matter-space framework of relativistic fluid dynamics. The central assumption is that the relevant degrees of freedom are encoded in differential forms on a three-dimensional matter space and mapped to spacetime by pull-back. The absence of four-forms in matter space imposes nontrivial kinematical constraints on the induced spacetime fields and restricts gauge transformations to those compatible with the flow. Because of this (matter-space) gauge symmetry, the physically relevant sector is retained, and the Aharonov-Bohm phase is naturally associated with the matter-space potential. The construction admits two electromagnetic frames. We argue that the frame identifying the spacetime field strength directly with the intrinsic matter-space two-form is geometrically preferred. In the first frame, the homogeneous sector is fixed by the matter-space structure, while the sourced equation follows from an action-based relativistic-fluid formulation in a first-order setting where the potential and field strength are varied independently and the matter-space constraints are imposed on shell. In the massless case and to quadratic order, locality and the (matter-space) gauge symmetry fix the leading field term in the action uniquely, so the resulting equations provide the minimal dynamical completion once charge carriers are included. We also clarify how duality controls the status of the Bianchi identity in the absence of magnetic charge carriers, and we briefly discuss helicity conservation and a natural nonlinear extension implied by the one-fluid constraints. In the second frame, on the other hand, the matter space 1-form is not directly related with the gauge potential.