Natural Science Forum / Physics / Research / October 2007

On Oct 14, 9:59 am, yy...@fas.harvard.edu wrote:

You should look at Chapter 6 in Rovelli's book "Quantum Gravity". Spin
networks (as functions of the Ashtekar connection on a 3-manifold)
define states that are gauge invariant. Defining an inner product on
these states, as described in Rovelli's book, and applying group
averaging with respect to spatial diffeomorphisms, reduces the space
of embedded labelled graphs to just abstract labelled graphs. These
are what's usually called "spin network states". By construction, they
are guague and spatial diffeomorphism invariant. But they do not
necessarily satisfy the Hamiltonian constraint. This latter constraint
has to be applied separately and this topic is still being actively
worked on (search for Thiemann's Master Constraint Program).

Hope this helps.

Igor