## Tuesday, November 08, 2005

Eectromagnetic-Torsion-Gravity Couplings

What do Becker & Shipov think? I do not have time for it at the moment.
On Nov 8, 2005, at 6:21 PM, art wagner wrote:

Go to (http://patft.uspto.gov/netahtml/srchnum.htm) and enter:
6,891,712 , a U.S. Patent of May 10, 2005; then GOOGLE the May 12,
2005 "United States Patent Application 20050099761" . Then see,
"...the electromagnetic field, through its energy-momentum tensor,
is also able to produce torsion, a point which is not in agreement
with the usual belief that only a spin distribution could be the
source of torsion. The crucial point of our approach is the
introduction of the teleparallel coupling prescription (50)...It is
not MINIMAL in the usual sense as such a name is currently reserved
for couplings of the form..." in
(http://arxiv.org/PS_cache/gr-qc/pdf/9708/9708051.pdf) and also the
(somewhat interesting)
(http://doc.cern.ch/archive/electronic/gr-qc/9612/9612061.pdf).

OK it's pretty simple really.

The exterior covariant derivative with torsion & curvature is simply

D = d + W/\ + S/\

W = curvature connection 1-form from locally gauging 4-parameter translation group T4

W = -*[dB/\(1 - B)]

* = Hodge dual from p-forms to 4 - p forms that depends on "metric" constituitive relations of the vacuum.

S = torsion connection 1-form from locally gauging O(1,3)

The U(1) EM is charge neutral

F = DA = dA + W/\A + S/\A

DF = 0

D*F = *J

D*J = 0

Are Maxwell's EM equations coupled to both curvature and torsion connection fields.

The Lagrangian density ~ F/\*F

Obviously all the fields couple together.

For Yang-Mills fields it's even more complicated. These classical c-number equations are straightforward.

We need to put in the lepton-quark spinor fields as well. They will be q-numbers on the c-number W & S background.

B = Lp'd'Phase

d'd' =/= 0 for a non-bounding 2-cycle surface S2 that surrounds a phase singularity where the intensity of the vacuum coherent wave form drops to zero in a point defect.

W = -*[dB/\(1 - B)]

B ~ Lp@^a(Pa/ih)(Goldstone Phase)

&a are the basic vector fields in the tangent LIF fiber

{Pa} is the 4-parameter @^a Lie algebra of T4.

S ~ -Lp^2@^a^bSab/h^2(Goldstone Phase)

{Sab} is the 6-parameter @^a^b Lie algebra of O(1,3).

This gives the DIMENSIONLESS PHASE 10 parameters {@^a, @^a^b} of Shipov's "oriented point".

Lp^2 = hG/c^3

The curvature equations are

R = DW = curvature 2-form

G = D*W 4-form

DR = 0 3-form

G = *J(curvature) 4-form

DG = D*J(curvature) = 0 5-form in 4-space is identically zero.

The torsion equations are

T = DS = torsion 2-form

DT = 0 3-form

D*S = *J(torsion) 4-form

D*J(torsion) = 0 5-form in 4-space.