Saturday, October 27, 2007

On Oct 27, 2007, at 10:28 PM, Kay zum Felde wrote:
This a paper by G.E. Volovik. I think it is meant as
an overview or summary of some basic aspects of
Volovik’s work. Its title is “Fermi point scenario for
emergent gravity.” It is only 10 pages which makes it
suitable as a compact on hand collection of the
cornerstones of his ideas concerning emergent gravity.
I think this might be his intention.

He underlines the need of emergent gravity theories
being based on vacua composed of chiral left plus
right Weyl fermions. Then Gravity emerges with matter.
He presents the, in his view, 10 basic consequences of
the Fermi point scenario. As I believe, that what
calls Fermi point scenario is a collection of aspects
that yield topologically stable emergence of defects,
e.g. matter, together with gravity.

He presents two distinct appearances of gravity, that
depend the relation of Planck’s energy vs. Lorentz
energy. These are classical hydrodynamics and
Einstein’s General Relativity.

As far as I understood this, he shares, at least in
general, some or many aspects with Jack’s theory.


In a general way yes, but not in detail. I do not use Fermi surface in momentum space. However my false vacuum is Minkowski so that a Fermi surface for virtual massless spin 1/2 Weyl spinors makes some sense. I do not see that Volovik has ODLRO.

Chapline has ODLRO but has many obscure premises. Visser also has an approach. None of them have my precise model getting the tetrads A^a and spin connections S^a^b from the coherent Goldstone vacuum phase 0-forms THETA^a & PHI^b just like the superflow velocity in Helium 4 below Lambda temperature - but more algebraically complicated - not much

A^a = M^a^a

S^a^b = M^[a,b]

M^a^b = dTHETA^a/\PHI^b - THETA^a/\dPHI^b

e^a = I^a + @A^a

@ is the fundamental dimensionless self-gravity coupling

ds^2 = guv(LNIF)dx^udx^v = (Minkowski LIF)abe^ae^b

Locally gauged Poincare group covariant partial derivative on source matter fields is

Du = e^auPa + S^a^bPab on matter source field Psi

Ten generators of Poincare group {Pa,Pab} are in same matrix irrep that source field Psi forms a basis of.

In 1905 SR in a GIF on Dirac spinors

e^a to I^a

I^aPa = i(Dirac Gamma Matrix)u&/&x^u

i.e. free particle Dirac equation in 1905 SR in the GIF is

{I^aPa + mc}Psi = 0 globally flat space-time

EQUIVALENCE PRINCIPLE dictates MINIMAL COUPLING so that Dirac equation for a neutral fermion in curved & torsioned space time is simply for Einstein-Cartan "unified field theory" beyond 1916 GR

{(I^a + @A^a)Pa + S^a^bPab}Psi = 0

The mean (expectation) value of the COM of this fermion moves on a curved & torsioned "autoparallel".
(Ehrenfest's theorem)

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