Thanks again!
1) Agreed about the typo. The negative sign is used because:
e sub a = (1, -1, -1, -1)
in the Cartesian basis and
B sup a = (B(0), B sub X, B sub Y, B sub Z)
Assuming that the vector B is spacelike, Eq. (12) gives in the Cartesian notation:
B bold = B sub X i bold + B sub Y j bold + B sub Z k bold
The results in the complex circular basis are given in the note. Agreed about Eq. (27), I fixed this typo later on.
5) Agreed. Eq. (9) is the elegant vector format of the Cartan identity derived in UFT254 and UFT255, and it transforms directly into Eq. (12), which is always true. Removal of indices gives the simple vector equation (16), and a new constraint in ECE theory. The latter can be either torsion or curvature based and this is a major new development in ECE theory.
The next stage in Notes for UFT316 is to develop the space part of the JCE identity to give new vector equations, then remove indices, in note 316(6). Then after checking UFT316 can be written up.
In a message dated 30/05/2015 17:51:33 GMT Daylight Time, writes:
In note 4, Eq. (3), there is a typo, T should be replaced by R.
Why did you use the negative sign in definition (12)?
In (27) the denominator W(0) should only occur in tthe Term A*B.note 5: If I see it right, eqs. 16,17 are always true, irrespective of
the existence of any magnetic monopoles. If A is not perpendicular to W,
the cross product must be divergence free.Horst