One of my still half-baked ideas merging inflation’s spontaneous breakdown of vacuum symmetry at the moment of creation of our observable universe patch -- at 0,0 in on Tamara Davis’s picture - this is the origin of our past particle horizon that is the future light cone of our Alpha Event Birth of Our Universe.
In string theory O(1,9) is the bosonic part of the bigger Poincare group , i.e. O(9) sub-group with 6 extra c-number dimensions. No supersymmetry here corresponding to using a spacetime manifold on quaternions.
In any case when
G = O(9) for spacelike slices
is spontaneous broken down to H = O(8)
i.e. degenerate vacuum manifold of O(9)/O(8) analogous to G = U1xSU2 ---> H = U1 in electro-weak standard model
dimO(9) - dimO(8) = 9 - 1 = 8 MASSLESS Goldstone phases
the SINGLE massive Higgs may be the /\ de Sitter scalar field?
the 8 massless Goldstone phases may connect to the 8 massless gluons of QCD’s SU3 by some analytic continuation from a non-compact spacetime symmetry group to the compact unitary group.
and I use the 8 massless phases of zero Cartan forms to get the four LIF Cartan 1-form tetrad gravity fields e^I via my M-Matrix trick.
On Jul 4, 2012, at 4:08 AM, JACK SARFATTI wrote:
More precisely in Weinberg’s example
spontaneous symmetry breaking of the vacuum (ground) state is
G = O(N) ---> H = O(N - 1) unbroken
(degenerate vacuum manifold is G/H of cosets for topological defect formation)
# massless Goldstone phase quantized oscillations is
dimG - dim H
which in this case is
(1/2)N(N - 1) - (1/2)(N - 1)(N - 2) = N - 1
In electro-weak
G = U(1)xSU(2), H = U(1)
dim G = 1 + 3 (number of charges)
dim H = 1
i.e. 3 massless Goldstone phase bosons eaten by W+, W-, Z
with one massive Higgs.
quarks and leptons have Yukawa couplings to the generalized coherent Glauber state (vacuum expectation value) of virtual (off-mass-shell) massive “amplitude” Higgs quanta.
In particle physics, Yukawa's interaction, named after Hideki Yukawa, is an interaction between a scalar field and a Dirac field.
The Yukawa interaction can be used to describe the strong nuclear force between nucleons (which are fermions), mediated by pions (which are pseudoscalar mesons). The Yukawa interaction is also used in the Standard Model to describe the coupling between the Higgs field and massless quark andlepton fields (i.e., the fundamental fermion particles). Through spontaneous symmetry breaking, these fermions acquire a mass proportional to the vacuum expectation value of the Higgs field.
http://en.wikipedia.org/wiki/Yukawa_interaction
Of course the GEV hadronic masses are from the confined ZPE of the virtual quark-antiquark/gluon plasma of Quantum Chromodynamics with the three real quarks have a relatively small Higgs field contribution. However, the electron is all Higgs field for its rest mass.
On Jul 4, 2012, at 3:43 AM, JACK SARFATTI wrote:
They still need to work on that it’s spin 0 and other details of its coupling to other particles. However, had they not found the peaks at ~ 125 Gev then the Standard Model would have been in deep doo doo.
Now on my earlier intuitive remarks on Higgs-Goldstone complementarity - more precisely:
For example in section 19.2 p. 168 of Volume II of Steven Weinberg's Magnum Opus "Quantum Theory of Fields" eqs 19.2.9 to 19.2.16 - for the O(N) symmetry group, with the quartic vacuum order parameter effective potential he proves N - 1 massless Goldstone phase spin 0 bosons an ONE massive spin zero Higgs boson. The simple intuitive U1 toy model in terms of AM & FM (actually PM) radio-radar analogy is the N = 2 case when I spoke of Glauber states with amplitude and phase complementary (canonically conjugate) to each other. The notion of a Glauber coherent state is generalizable for any continuous Lie Group not only U1 ~ O(2).
On Jul 4, 2012, at 2:15 AM, JACK SARFATTI wrote:
Jack Sarfatti
2 seconds ago near San Francisco
with Marshall Stoneham (1967). "The Goldstone Theorem in the Jahn-Teller Effect", Proceedings of the Physical Society of London, Vol. 91, No. 1, cited in American Institute of Physics Resource Letter on Symmetry in Physics, 1980 (at Atomic Energy Research Establishment, Harwell, Didcot, Berks).
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Jack Sarfatti MY PAPER FROM 1967 AT UNITED KINGDOM ATOMIC ENERGY RESEARCH ESTABLISHMENT HARWELL DIDCOT, BERKS WITH THE LATE MARSHALL STONEHAM - DUE TO MY VISITS TO IMPERIAL COLLEGE, LONDON WHERE ABDUS SALAM AND T. KIBBLE WERE WORKING ON THE HIGGS IDEA.
ABDUS SALAM INVITED ME TO TRIESTE IN 1973