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Theoretical Universe
Table of Contents:
Licence
How to cite
How to contribute
Resources
The Cartan-Hodge formalism
Basis vectors
Musicality
Hodge duality fundamentals
Hodge dual computations
Free matrix representation
Minkowski metric
Rotations in differential form
Rotations in Euclidean space
Rotations in Minkowski space
Exponential map
Differential operators expressed as exterior derivatives
3D Euclidean space
Minkowski space
0–forms (functions)
1–forms (translations)
2–forms (rotations)
3–forms (3D volumes)
4–forms (4D volumes)
Covariant formulation of the electromagnetic field
Revisiting the 1865 Maxwell’s equations
Deriving the Faraday tensor from the 1865 Maxwell’s equations
Deriving the Faraday 2–form from the 1865 Maxwell’s equations
Relation between the Faraday 2–form and the Faraday tensor
Potential formulation via differential forms
All electromagnetic field forms
Random thoughts
Proving De Gua’s theorem with Clifford algebra
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3–forms (3D volumes)
3–forms (3D volumes)
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by Stéphane Haussler
Warning
Under construction