Kaiser's paper 81JMP.pdf on his website
"Phase Space Approach to Relativistic Quantum Mechanics III"
http://www.wavelets.com/vita.html#papers
is of particular interest for several reasons.

The Lie algebra for the 10 "charges" of the globally flat "false"
Minkowski space-time vacuum's Poincare group is

[Ji,Jj] = Jk

[To,Kr] = Tr

[Ki,Kj] = -c^-2Jk

[Ji,Kj] = Kk

[Ji,Tj] = Tk

[Tr,Ks] = -c^-2&rsTo

where i,j,k = 1,2,3 (or x,y,z in Cartesian frame of high school analytic
geometry)
(ijk) above in sense of cyclic permutation

r,s = 1,2,3

To is total energy generating time translations in globally flat
Minkowski spacetime

Tk = total linear momentum generating space translations

Jk are space-components of total angular momentum generating space
rotations along the k space axis in the ij space plane.

Kk are the Lorentz boosts between two Global Inertial Frames along the k
axis in space, which, by definition, are not accelerated frames. These
are space-time rotations (0,k) in Minkowski space-time.

The Poincare group is a "semi-direct" product of the translation
subgroup Lie algebra {To, T1,T2,T3} with the Lorentz O(1,3) subgroup Lie
algebra {J1,J2,J3,K1,K2,K3}. Since the commutators across the two
subgroups do not commute.

Note that the Galilean limit of Newtonian mechanics is c - infinity where

[Ki,Kj] = -c^-2Jk -- 0

and

[Tr,Ks] = -c^-2&rsTo -- 0

Now Kibble showed (mid 1960's) that Einstein's 1915 theory of gravity
without torsion fields comes from locally gauging the 4 generators {T0,
T1, T2, T3}. This can be seen heuristically in the large scale L Lp
limit of Hagen Kleinert's "world crystal lattice" elastic-plastic model
of General Relativity.

Globally flat 4D Minkowski space-time is simply a perfectly tiled
lattice with unit cells at the Planck scale Lp. The symmetry of these
unit cells is washed out in the large scale L Lp.

The compensating gauge force fields for {T0, T1, T2, T3} are simply
du(x), i.e. the distortion field of the world crystal at point x.

Hagen Kleinert then shows that Einstein's 1915 theory comes from the
strain tensor of the distorted world crystal

guv = Minkowski metric + (1/2)[du(x),v + dv(x),u]

with string defects of disclination whose large scale density is
precisely Einstein's tidal force curvature tensor.

The global translation group symmetry is broken, but is replaced by the
Diff(4) local symmetry group. EEP is obeyed in the tetrad eu^a(x)
formulation of the theory where u is in the curved base spacetime and a
is in the locally almost flat tangent spacetime. "Almost" means we are
far enough from a spacetime black hole singularity and larger than Lp so
that tidal curvature g-force differentials and quantum gravity
fluctuations are ignorable. Note, that the g-force is eliminated in
LIFs on timelike geodesics, but the tidal differential curvature force
from geodesic deviation is not eliminated. However, EEP only holds in
the "weak curvature" non micro-quantum domain. That Einstein may not
have realized this limitation on his theory in the early days is of no
great consequence IMHO. I am not even sure that he did not realize it at
least after 1925. I am alluding, of course, to Paul Zielinski's thesis
that may be a valid footnote in the history of the emergence of
Einstein's thought. If one wants a local stress energy density tensor
for geometry it is simply

Tuv(Geometry) = (String Tension)Guv

Define the non-exotic vacuum as

Tuv(matter/radiation/near EM fields) = 0

/\zpf = 0

And in that case

Tuv(Geometry) = 0.

However, in the exotic w = -1 "zero point energy density" dark
energy/matter vacuum

Tuv(Geometry) +(String Tension) /\zpfguv = 0

Metric engineering in the exotic vacuum is

Tuv(Geometry)^;v =/= 0

Tuv(Geometry)^;v + /\zpf^,vguv = 0

assuming metricity and zero torsion in this simplest of cases.

/\zpf = (alpha')^-1[(alpha')^3/2|Vacuum Coherence|^2 - 1]

h = c = 1 convention temporarily

alpha' = (String Tension)^-1 = Witten parameter

There is no need for the Yilmaz theory.

See below on Vacuum Coherence quieting the random chaos of the
micro-quantum field vacuum zero point fluctuations. This insight is
entirely missing from current string theory as well as the program of
Haisch and Puthoff. In the former case we have Ed Witten admitting that
the smallness of the Cosmological Constant is very serious for his M
Theory. In contrast Hal Puthoff simply hand waves away the problem,
which simply will not do IMHO.

Kleinert does not have any connection to quantum theory in his model.

I have added that.

My MACRO-QUANTUM Coherent Ansatz is:

du(x) = Lp^2(Goldstone Phase(x)),u

,u = partial derivative

where

Vacuum Coherence Field = (Higgs Amplitude Field)e^i(Goldstone Phase Field)

I also have a micro-quantum "BCS" type argument why this macro local
field emerges from the QED sector of quantum field theory at least as a
low energy approximate effective ODLRO c-number smooth field theory.

This Vacuum Coherence Field is the scalar field of inflationary
cosmology in the FRW limit.

The Lp^2 is consistent with Black Hole Thermodynamics of Bekenstein et-al.

Back to the Lie Algebra, we see that there are non-vanishing commutators
between the translation and the Lorentz subgroup algebras. Therefore,
completeness and consistency (not in Godel's sense) suggest that we must
also locally gauge the Lorentz group. Utiyama showed, before Kibble,
that locally gauging the entire Poincare group gives a larger theory
than Einstein's with the additional torsion field as the compensating
gauge force field from the 6 charges
{J1,J2,J3,K1,K2,K3}. The torsion field appears as an antisymmetric
Diff(4) 3rd rank tensor additional piece of the connection field for
parallel transport of Diff(4) tensors along world lines in curved spacetime.

The De Sitter group has a curvature parameter that is really Einstein's
"cosmological constant" /\ in the sense of the FRW metric. Now
apparently /\ - infinity has Penrose's 15 parameter "conformal group"
of massless twistors as the limit and there is a kind of string duality

/\' ~ Lp^4//\

between zero and infinite cosmological constants which I suspect are at
best "metastable" vacua.

So the issue is additional compensating gauge force fields by locally
gauging the entire Lie Algebra of the De Sitter group, which obviously
will give the local /\zpf(x) unified dark energy/matter field and
perhaps something extra?

Where can I find the Lie algebra of the De Sitter Group fully written out?

On Monday, November 17, 2003, at 09:37 PM, Tony Smith wrote:

Jack, you ask:
"... 4 special conformal generators ...
What do they locally gauge to?
My hunch is /\zpf,u ...".

Yes, I think so too, and have written some stuff about it
on my web page at
http://www.innerx.net/personal/tsmit...ngraviton.html

The basic reference for that work is a paper by Aldrovandi and Pereira at
http://xxx.lanl.gov/abs/gr-qc/9809061
which describes in some detail how the special conformal group
gives rise to cosmological "constant" type terms.
My contribution, built on their nice math foundation,
is to count degrees of freedom and get a result that
at a critical time in the past the ratio of "matter forms" in
our universe should have been:

67% Dark Energy
27% Dark Matter
6% Ordinary Matter

and if you follow evolution in ways that seem reasonable to me,
you get a present-day content in a range of (depending on whether
Cold Dark Matter is in the form of Primordial Black Holes,
or MOND, or a mixture thereof):

68-75% Dark Energy
28-21% Dark Matter
4% Ordinary Matter

The observed composition by WMAP:

73% Dark Energy
23% Dark Matter
4% Ordinary Matter

is between the 75-21-4 result of assuming Cold Dark Matter is
made up of Primordial Black Holes,
and
to the 71-25-4 result of assuming that Cold Dark Matter is
a (reasonable to me) mixture of Primordial Black Holes and MOND.

Unfortunately from my point of view, I cannot put these results
on the Cornell arXiv because I am blacklisted.
It is especially unfortunate because they indicate that your
model is on the right track (except that I don't like the naive
form of supersymmetry that exists in superstring theory).

Tony