43 research outputs found
Physical boundary state for the quantum tetrahedron
We consider stability under evolution as a criterion to select a physical
boundary state for the spinfoam formalism. As an example, we apply it to the
simplest spinfoam defined by a single quantum tetrahedron and solve the
associated eigenvalue problem at leading order in the large spin limit. We show
that this fixes uniquely the free parameters entering the boundary state.
Remarkably, the state obtained this way gives a correlation between edges which
runs at leading order with the inverse distance between the edges, in agreement
with the linearized continuum theory. Finally, we give an argument why this
correlator represents the propagation of a pure gauge, consistently with the
absence of physical degrees of freedom in 3d general relativity.Comment: 20 pages, 6 figure
Grasping rules and semiclassical limit of the geometry in the Ponzano-Regge model
We show how the expectation values of geometrical quantities in 3d quantum
gravity can be explicitly computed using grasping rules. We compute the volume
of a labelled tetrahedron using the triple grasping. We show that the large
spin expansion of this value is dominated by the classical expression, and we
study the next to leading order quantum corrections.Comment: 18 pages, 1 figur
Numerical indications on the semiclassical limit of the flipped vertex
We introduce a technique for testing the semiclassical limit of a quantum
gravity vertex amplitude. The technique is based on the propagation of a
semiclassical wave packet. We apply this technique to the newly introduced
"flipped" vertex in loop quantum gravity, in order to test the intertwiner
dependence of the vertex. Under some drastic simplifications, we find very
preliminary, but surprisingly good numerical evidence for the correct classical
limit.Comment: 4 pages, 8 figure
N=2 supersymmetric spin foams in three dimensions
We construct the spin foam model for N=2 supergravity in three dimensions.
Classically, it is a BF theory with gauge algebra osp(2|2). This algebra has
representations which are not completely reducible. This complicates the
procedure when building a state sum. Fortunately, one can and should excise
these representations. We show that the restricted subset of representations
form a subcategory closed under tensor product. The resulting state-sum is once
again a topological invariant. Furthermore, within this framework one can
identify positively and negatively charged fermions propagating on the spin
foam. These results on osp(2|2) representations and intertwiners apply more
generally to spin network states for N=2 loop quantum supergravity (in 3+1
dimensions) where it allows to define a notion of BPS states.Comment: 12 page
Consistently Solving the Simplicity Constraints for Spinfoam Quantum Gravity
We give an independent derivation of the Engle-Pereira-Rovelli spinfoam model
for quantum gravity which recently appeared in [arXiv:0705.2388]. Using the
coherent state techniques introduced earlier in [arXiv:0705.0674], we show that
the EPR model realizes a consistent imposition of the simplicity constraints
implementing general relativity from a topological BF theory.Comment: 6 pages, 2 figures, v2: typos correcte
Twistorial phase space for complex Ashtekar variables
We generalise the SU(2) spinor framework of twisted geometries developed by
Dupuis, Freidel, Livine, Speziale and Tambornino to the Lorentzian case, that
is the group SL(2,C). We show that the phase space for complex valued Ashtekar
variables on a spinnetwork graph can be decomposed in terms of twistorial
variables. To every link there are two twistors---one to each boundary
point---attached. The formalism provides a new derivation of the solution space
of the simplicity constraints of loop quantum gravity. Key properties of the
EPRL spinfoam model are perfectly recovered.Comment: 18 pages, to appear in: Class. Quantum Gra
Revisiting the Simplicity Constraints and Coherent Intertwiners
In the context of loop quantum gravity and spinfoam models, the simplicity
constraints are essential in that they allow to write general relativity as a
constrained topological BF theory. In this work, we apply the recently
developed U(N) framework for SU(2) intertwiners to the issue of imposing the
simplicity constraints to spin network states. More particularly, we focus on
solving them on individual intertwiners in the 4d Euclidean theory. We review
the standard way of solving the simplicity constraints using coherent
intertwiners and we explain how these fit within the U(N) framework. Then we
show how these constraints can be written as a closed u(N) algebra and we
propose a set of U(N) coherent states that solves all the simplicity
constraints weakly for an arbitrary Immirzi parameter.Comment: 28 page
Coupling gauge theory to spinfoam 3d quantum gravity
We construct a spinfoam model for Yang-Mills theory coupled to quantum
gravity in three dimensional riemannian spacetime. We define the partition
function of the coupled system as a power series in g_0^2 G that can be
evaluated order by order using grasping rules and the recoupling theory. With
respect to previous attempts in the literature, this model assigns the
dynamical variables of gravity and Yang-Mills theory to the same simplices of
the spinfoam, and it thus provides transition amplitudes for the spin network
states of the canonical theory. For SU(2) Yang-Mills theory we show explicitly
that the partition function has a semiclassical limit given by the Regge
discretization of the classical Yang-Mills action.Comment: 18 page
Holomorphic Simplicity Constraints for 4d Spinfoam Models
Within the framework of spinfoam models, we revisit the simplicity
constraints reducing topological BF theory to 4d Riemannian gravity. We use the
reformulation of SU(2) intertwiners and spin networks in term of spinors, which
has come out from both the recently developed U(N) framework for SU(2)
intertwiners and the twisted geometry approach to spin networks and spinfoam
boundary states. Using these tools, we are able to perform a
holomorphic/anti-holomorphic splitting of the simplicity constraints and define
a new set of holomorphic simplicity constraints, which are equivalent to the
standard ones at the classical level and which can be imposed strongly on
intertwiners at the quantum level. We then show how to solve these new
holomorphic simplicity constraints using coherent intertwiner states. We
further define the corresponding coherent spin network functionals and
introduce a new spinfoam model for 4d Riemannian gravity based on these
holomorphic simplicity constraints and whose amplitudes are defined from the
evaluation of the new coherent spin networks.Comment: 27 page
A semiclassical tetrahedron
We construct a macroscopic semiclassical state state for a quantum
tetrahedron. The expectation values of the geometrical operators representing
the volume, areas and dihedral angles are peaked around assigned classical
values, with vanishing relative uncertainties.Comment: 10 pages; v2 revised versio