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 be a compact oriented Riemannian manifold of dimension . Write for the corresponding Hodge star operator.
Then for every exact differential n-form of degree there is in each de Rham cohomology class of degree k a unique representative closed k-form
such that
Reading this as Maxwell's equations on then is the field of gravity, is the Faraday tensor measuring the field strength of the electromagnetic field and 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.