5 research outputs found
A spin foam model for general Lorentzian 4-geometries
We derive simplicity constraints for the quantization of general Lorentzian
4-geometries. Our method is based on the correspondence between coherent states
and classical bivectors and the minimization of associated uncertainties. For
spacelike geometries, this scheme agrees with the master constraint method of
the model by Engle, Pereira, Rovelli and Livine (EPRL). When it is applied to
general Lorentzian geometries, we obtain new constraints that include the EPRL
constraints as a special case. They imply a discrete area spectrum for both
spacelike and timelike surfaces. We use these constraints to define a spin foam
model for general Lorentzian 4-geometries.Comment: 27 pages, 1 figure; v4: published versio
Generating Functions for Coherent Intertwiners
We study generating functions for the scalar products of SU(2) coherent
intertwiners, which can be interpreted as coherent spin network evaluations on
a 2-vertex graph. We show that these generating functions are exactly summable
for different choices of combinatorial weights. Moreover, we identify one
choice of weight distinguished thanks to its geometric interpretation. As an
example of dynamics, we consider the simple case of SU(2) flatness and describe
the corresponding Hamiltonian constraint whose quantization on coherent
intertwiners leads to partial differential equations that we solve.
Furthermore, we generalize explicitly these Wheeler-DeWitt equations for SU(2)
flatness on coherent spin networks for arbitrary graphs.Comment: 31 page
Spin foams with timelike surfaces
Spin foams of 4d gravity were recently extended from complexes with purely
spacelike surfaces to complexes that also contain timelike surfaces. In this
article, we express the associated partition function in terms of vertex
amplitudes and integrals over coherent states. The coherent states are
characterized by unit 3--vectors which represent normals to surfaces and lie
either in the 2--sphere or the 2d hyperboloids. In the case of timelike
surfaces, a new type of coherent state is used and the associated completeness
relation is derived. It is also shown that the quantum simplicity constraints
can be deduced by three different methods: by weak imposition of the
constraints, by restriction of coherent state bases and by the master
constraint.Comment: 22 pages, no figures; v2: remarks on operator formalism added in
discussion; correction: the spin 1/2 irrep of the discrete series does not
appear in the Plancherel decompositio