Pair and impair, even and odd form fields, and electromagnetism
Article first published online: 16 DEC 2009
Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Annalen der Physik
Volume 19, Issue 1-2, pages 6–34, February 2010
How to Cite
da Rocha, R. and Rodrigues, W.A. (2010), Pair and impair, even and odd form fields, and electromagnetism. Ann. Phys., 19: 6–34. doi: 10.1002/andp.200910374
- Issue published online: 27 JAN 2010
- Article first published online: 16 DEC 2009
- Manuscript Accepted: 24 AUG 2009
- Manuscript Revised: 13 AUG 2009
- Manuscript Received: 2 FEB 2009
- Clifford bundle;
- Maxwell's equations.
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 metric-free approach becomes a single equation is compatible with both formulations of electromagnetism just mentioned above. In addition 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.