**Subject:** Shorthand Notation for ECE Theory

**Date:** Sun, 22 Mar 2009 12:16:11 EDT

This notation is frequently used in the ECE papers and brings concepts down to barebone essentials. In this notation the most important equations of Cartan’s geometry are simple and are as follows.

1) First Cartan structure equation,

T = D ^ q = d ^ q + omega ^ q

here T is a symbol that denotes torsion, D ^ denotes covariant exterior derivative, d ^ denotes exterior derivative, omega denotes spin connection, q denotes the Cartan tetrad.

2) Electrodynamical field potential relation

F = D ^ A

3) Second Cartan structure equation

R = D ^ omega

where R is the curvature.

4) The Cartan Bianchi identity

D ^ T := R ^ q = q ^ R

This gives the homogeneous field equations of both dynamics and electrodynamics.

5) The Cartan Evans Dual Identity

D ^ T tilde := R tilde ^ q = q ^ R tilde.

This gives the inhomogeneous field equations. The identity and dual identity are Hodge invariant because one is simply an example of the other.

6) The tetrad postulate

Dq = 0

which gives all the wave equations of physics and unifies quantum mechanics and general relativity. The D without the ^ symbol means covariant derivative with spin connection.

7) The basic hypotheses of ECE theory

A = A(0)q; J = (c / k) T

Memorize these and you have physics in a nutshell. As advocated by that great heretic William of Ockham, physics is simple. He was due to be made into a candle, but was protected by Ludwig of Bavaria. Then all 127 ECE source papers follow, plus many other excellent papers by now from capable ECE scholars.

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