**Subject:** 131(3): The Commutator and ECE Electromagnetic Field Density

**Date:** Tue, 28 Apr 2009 05:44:41 EDT

This note points out that, in four dimensions, the commutator of covariant derivatives generates both the electromagnetic and gravitational field densities through eqs. (24) and its Hodge invariant, eq. (26). In the now obsolete gauge theory of the twentieth century such as procedure is also used, but an abstract gauge space is used without realizing the presence of curvature. Eq. (6) of this note defines the correct antisymmetry of the connection. This will lead in this paper to new antisymmetry relations between components of the electromagnetic potential. For example, in the well known

E = – del phi – partial A / partial t

of the U(1) level of electromagnetism, there are antisymmetry relations between the first and second term:

del phi = – partial A / partial t

which clear up problems going back to Heaviside. These relations remove the need for the Lorenz gauge and have been missed for about one hundred and forty years. Similarly, the incorrect symmetric connection in gravitation was used for over a hundred years and tremendously complicated claims built on incorrect basics. These notes give a lot of detail, and should be understandable to chemists and engineers. Theoretical physicists have the habit of looking down on their colleagues in chemistry and engineering as second class citizens, but theoretical physicists should reflect on what they produce these days. It is often not recognizable as science at all.

Attachment: a131stpapernotes3.pdf