physics, mathematical physics, philosophy of physics
theory (physics), model (physics)
experiment, measurement, computable physics
Axiomatizations
Tools
Structural phenomena
Types of quantum field thories
The Hodge theorem in the language of electromagnetism. Over a Riemann surface this may be regarded as simple case of the Narasimhan-Seshadri theorem.
Let $(X,g)$ be a compact oriented Riemannian manifold of dimension $n$. Write $\star$ for the corresponding Hodge star operator.
Then for every exact differential n-form $j$ of degree $n-k-1$ there is in each de Rham cohomology class of degree k a unique representative closed k-form $F$
such that
Reading this as Maxwell's equations on $(X,g)$ then $g$ is the field of gravity, $F$ is the Faraday tensor measuring the field strength of the electromagnetic field and $j$ is the electric current.
The term “Hodge-Maxwell theorem” in the above form appears in
Last revised on February 12, 2024 at 15:25:41. See the history of this page for a list of all contributions to it.