Dirac equation in the algebra of physical space Dirac equation in the algebra of physical space The Dirac equation, as the relativistic equation that describes spin 1/2 particles in quantum mechanics, can be written in terms of the Algebra of physical space (APS), which is a case of a Clifford algebra or geometric algebra that is based on the use of paravectors. The Dirac equation in APS, including the electromagnetic interaction, reads Another form of the Dirac equation in terms of the Space time algebra was given earlier by David Hestenes. In general, the Dirac equation in the formalism of geometric algebra has the advantage of providing a
Algebra of physical space equation, for an electrically charged particle of mass "m" and charge "e", takes the form: where e is an arbitrary unitary vector, and "A" is the electromagnetic paravector potential as above. The electromagnetic interaction has been included via minimal coupling in terms of the potential "A". The differential equation of the Lorentz rotor that is consistent with the Lorentz force is such that the proper velocity is calculated as the Lorentz transformation of the proper velocity at rest which can be integrated to find the space-time trajectory formula_31 with the additional use of Algebra of physical space In physics, the