Electromagnetic field modeling through the use of Dirac matrices and geometric algebra

The basis for engineering electromagnetic computations still rely on Gibbs' vector algebra. It is well known that Clifford algebra (geometric algebra) presents several enhancement on the latter. By taking advantage that in the three-dimensional space Clifford algebra is isomorphic to Pauli algebra it is possible to describe all the relevant vector operations occurring in electromagnetic theory in terms of Pauli matrices. In particular it is possible to write Maxwell's equations in a form similar to the Dirac equation. In this way, instead of having six coupled equations from the curls operators, we can deal with just four linear equations. The latter can be further simplified to just two sets of two linear equations by the Weyl decomposition.