where the components of
are related to those of the usual curvature tensor by
Although the underlying gauge potentials
are
o
(3,2)- or
o
(4,1)-valued, the action is only invariant under the
6-dimensional subgroup of Lorentz transformations. The theory
contains a dimensionful parameter
l
. The gauge potentials associated with the internal 5-direction
are identified with the frame fields
, and the action can be decomposed into the usual Einstein-term
(1
) plus a cosmological constant term with
and a topological
-term. Smolin analyzed its lattice discretization, and found
both a weak- and a strong-coupling phase, with respect to the
dimensionless coupling constant
. He performed a weak-coupling expansion about flat space and
rederived the usual propagator. In the strong-coupling regime he
found massive excitations and a confining property for
spinors.
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Discrete Approaches to Quantum Gravity in Four Dimensions
Renate Loll http://www.livingreviews.org/lrr-1998-13 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |