http://rst.gsfc.nasa.gov/Sect20/A10.html (background info)
Yang-Mills gauge forces are spin 1 renormalizable as quantum fields, which is good. Gravity as a spin 2 field is not quantum renormalizable, which is bad. However, we have seen that gravity's tetrad substratum is also spin 1 and that spin 2 is a composite along with spin 1 and spin 0 quantum corrections not seen in the classical theory. The fundamental gravity gauge field is the spin 1 warped tetrad A^a where Einstein's metric field is e^aea = (I^a + @A^a)(Ia + @Aa) with, like QED fine structure e^2/hc ~ 1/137, @ a dimensionless coupling (Lp^2/\zpf)^1/3 with /\zpf = Lenny Susskind's "cosmological landscape height" in IR limit. In our Hubble deSitter horizon pocket universe
on the Linde eternal chaotic inflation landscape (c^4/G)/\zpf ~ (10^-3ev)^4.
/\zpf is the vertical height here
where (Lp^2/\zpf)1/3 ~ (10^-66 10^-56)^1/3 ~ 10^-41 = Eddington number. I get 1/3 from world hologram conjecture.
1. For 1916 GR the zero torsion connection is derived from the metric field.
2. There is no equivalence principle for Yang-Mills fields unless one uses null geodesics in extra-dimensional hyperspace - Kaluza-Klein --> M theory.
3. L(Einstein-Hilbert) is ~ R linear in "field strength".
But that depends on what is meant - at substratum level R is quadratic in F^a = de^a.
Connection ~ e^aeb,u
Curvature ~ (e^aeb)[,u,v] + non-Abelian curl terms
R^a^b = dS^a^b + S^ac/\S^cb
0 = de^a + S^ac/\e^c
de^a = dI^a + @dA^a = dI^a + F^a
F^a is the gravity substratum "Yang-Mills" 2-form "field"
F^a = - S^ac/\A^c
with zero torsion.
On Jun 3, 2007, at 5:00 PM, Jack Sarfatti wrote:
PS To be more precise: Let Psi be the matter source fields forming a basis for an irreducible representation R of the rigid global Lie group G where the action field density L invariant under G. We need a new larger action density L' invariant under the larger locally gauged G(x) where the parameters of G are no longer constants but are arbitrary functions of the overlapping local coordinate charts. L(Psi, Psi,u) -> L(Psi, R(DuPsi), Au) where Au is the spin 1 compensating gauge field "connection".
GR is less direct than Yang-Mills because of the equivalence between local g-forces and stationary non-geodesic observers outside of event horizons. Not all GeoMetroDynamic fields are stationary of course - but the non-stationary corrections (gravity waves) are usually pretty small - definitely small Earthside. In GR the passive no gravity arena for Yang-Mills fields becomes at active player. A^a is the warped tetrad connection. It is spin 1 as a quantum field. The GMD affine connection is secondary essentially (,u is ordinary partial derivative):
GMD connection of Einstein-Cartan theory ~ e^ae^b,u = (I^a + @A^a)(I^b + @A^b),u
this includes possible torsion fields, but not a non-metricity Weyl conformal boost field in which the inner products are anholonomic (path dependent) - the non-metricity 4-potential has no relation to the EM potential which was Weyl's error of 1918. The curl of this conformal boost 4-potential vanishes in a simply connected way for phenomena observed so far.