Classical Electrodynamics
The electromagnetic field is represented as a bi-paravector, with the Hermitian part representing the Electric field and the anti-Hermitian part representing the magnetic field. In the standard Pauli matrix representation, the electromagnetic field is
The electromagnetic field is obtained from the paravector potential as
and the electromagnetic field is invariant under a gauge transformation of the form
where is a scalar function.
The Electromagnetic field is covariant under Lorentz transformations according to the law
The Maxwell equations can be expressed in a single equation as follows
where the overbar represents the Clifford conjugation and the four-current is defined as
The electromagnetic Lagrangian is
which is evidently a real scalar invariant.
The Lorentz force equation takes the form
Read more about this topic: Algebra Of Physical Space
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