Pair and Impar, Even and Odd Form Fields and Electromagnetism

TL;DR

This paper demonstrates that electromagnetism can be coherently formulated using only pair differential form fields in relativistic spacetime, challenging previous claims and unifying different mathematical descriptions without observable physical differences.

Contribution

It proves the possibility of formulating electromagnetism solely with pair form fields in relativistic spacetime and unifies Maxwell equations in the Clifford bundle formalism.

Findings

Electromagnetism can be formulated with only pair form fields.

A unified Maxwell equation in Clifford formalism is compatible with both formulations.

Derived the force density directly from Maxwell's equations.

Abstract

In this paper after reviewing the Schouten and de Rham definition of impair and pair differential form fields (not to be confused with differential form fields of even and odd grades) we prove that in a relativistic spacetime it is possible (despite claims in contrary) to coherently formulate electromagnetism (and we believe any other physical theory) using only pair form fields or, if one wishes, using pair and impair form fields together, in an appropriate way. Those two distinct descriptions involve only a mathematical choice and do not seem to lead to any observable physical consequence if due care is taken. Moreover, we show in details that a formulation of electromagnetic theory in the Clifford bundle formalism of differential forms where the two Maxwell equations of the so called free metric approach becomes a single equation is compatible with both formulations of electromagnetism just mentioned above. Moreover we derive directly from Maxwell equation the density of force (coupling of the electromagnetic field with the charge current) that is a postulate in the free metric approach to electromagnetism. We recall also a formulation of the engineering version of Maxwell equations using electric and magnetic fields as objects of the same nature, i.e., without using polar and axial vectors.