📝 SummarXiv

Abstract

We develop a matter-space framework in which particles including photons are modeled as residing on a three-dimensional matter space, while the familiar electromagnetic fields in four-dimensional spacetime arise as projections. A set of constraint equations, implied by the absence of nontrivial 4-forms on a three-dimensional space, yields a ``matter-space gauge symmetry'', which manifests on a subset of the 1-form fields in 4-dimensional spacetime. Employing the electro-magnetic duality, the gauge symmetry enforces a precise relation between the potential $A_a$ and the field strength $F_{ab}$, reproducing one half of Maxwell's equations. The remaining Maxwell equation follows from an action principle for relativistic fluids formulated on matter space. Notably, in this construction the dynamics of electromagnetism emerges from the set of constraints, rather than being added ad hoc. This formulation not only ensures consistency with conventional electromagnetism but also provides deeper insights on the particle nature of the electromagnetic field. To support this claim, we demonstrate that i) the Aharonov-Bohm effect arises solely from the matter-space gauge potential. ii) the helicity is shown to be conserved automatically. iii) nonlinear corrections analogous to mass renormalization are intrinsically incorporated. This framework offers a fundamental interplay between matter and electromagnetic fields.