18 research outputs found
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
Non-commutative flux representation for loop quantum gravity
The Hilbert space of loop quantum gravity is usually described in terms of
cylindrical functionals of the gauge connection, the electric fluxes acting as
non-commuting derivation operators. It has long been believed that this
non-commutativity prevents a dual flux (or triad) representation of loop
quantum gravity to exist. We show here, instead, that such a representation can
be explicitly defined, by means of a non-commutative Fourier transform defined
on the loop gravity state space. In this dual representation, flux operators
act by *-multiplication and holonomy operators act by translation. We describe
the gauge invariant dual states and discuss their geometrical meaning. Finally,
we apply the construction to the simpler case of a U(1) gauge group and compare
the resulting flux representation with the triad representation used in loop
quantum cosmology.Comment: 12 pages, matches published versio
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
A Note on B-observables in Ponzano-Regge 3d Quantum Gravity
We study the insertion and value of metric observables in the (discrete) path
integral formulation of the Ponzano-Regge spinfoam model for 3d quantum
gravity. In particular, we discuss the length spectrum and the relation between
insertion of such B-observables and gauge fixing in the path integral.Comment: 17 page
A New Class of Group Field Theories for 1st Order Discrete Quantum Gravity
Group Field Theories, a generalization of matrix models for 2d gravity,
represent a 2nd quantization of both loop quantum gravity and simplicial
quantum gravity. In this paper, we construct a new class of Group Field Theory
models, for any choice of spacetime dimension and signature, whose Feynman
amplitudes are given by path integrals for clearly identified discrete gravity
actions, in 1st order variables. In the 3-dimensional case, the corresponding
discrete action is that of 1st order Regge calculus for gravity (generalized to
include higher order corrections), while in higher dimensions, they correspond
to a discrete BF theory (again, generalized to higher order) with an imposed
orientation restriction on hinge volumes, similar to that characterizing
discrete gravity. The new models shed also light on the large distance or
semi-classical approximation of spin foam models. This new class of group field
theories may represent a concrete unifying framework for loop quantum gravity
and simplicial quantum gravity approaches.Comment: 48 pages, 4 figures, RevTeX, one reference adde
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
Observables in 3d spinfoam quantum gravity with fermions
We study expectation values of observables in three-dimensional spinfoam
quantum gravity coupled to Dirac fermions. We revisit the model introduced by
one of the authors and extend it to the case of massless fermionic fields. We
introduce observables, analyse their symmetries and the corresponding proper
gauge fixing. The Berezin integral over the fermionic fields is performed and
the fermionic observables are expanded in open paths and closed loops
associated to pure quantum gravity observables. We obtain the vertex amplitudes
for gauge-invariant observables, while the expectation values of gauge-variant
observables, such as the fermion propagator, are given by the evaluation of
particular spin networks.Comment: 32 pages, many diagrams, uses psfrag
Coherent states, constraint classes, and area operators in the new spin-foam models
Recently, two new spin-foam models have appeared in the literature, both
motivated by a desire to modify the Barrett-Crane model in such a way that the
imposition of certain second class constraints, called cross-simplicity
constraints, are weakened. We refer to these two models as the FKLS model, and
the flipped model. Both of these models are based on a reformulation of the
cross-simplicity constraints. This paper has two main parts. First, we clarify
the structure of the reformulated cross-simplicity constraints and the nature
of their quantum imposition in the new models. In particular we show that in
the FKLS model, quantum cross-simplicity implies no restriction on states. The
deeper reason for this is that, with the symplectic structure relevant for
FKLS, the reformulated cross-simplicity constraints, in a certain relevant
sense, are now \emph{first class}, and this causes the coherent state method of
imposing the constraints, key in the FKLS model, to fail to give any
restriction on states. Nevertheless, the cross-simplicity can still be seen as
implemented via suppression of intertwiner degrees of freedom in the dynamical
propagation. In the second part of the paper, we investigate area spectra in
the models. The results of these two investigations will highlight how, in the
flipped model, the Hilbert space of states, as well as the spectra of area
operators exactly match those of loop quantum gravity, whereas in the FKLS (and
Barrett-Crane) models, the boundary Hilbert spaces and area spectra are
different.Comment: 21 pages; statements about gamma limits made more precise, and minor
phrasing change
Reconstructing Quantum Geometry from Quantum Information: Spin Networks as Harmonic Oscillators
Loop Quantum Gravity defines the quantum states of space geometry as spin
networks and describes their evolution in time. We reformulate spin networks in
terms of harmonic oscillators and show how the holographic degrees of freedom
of the theory are described as matrix models. This allow us to make a link with
non-commutative geometry and to look at the issue of the semi-classical limit
of LQG from a new perspective. This work is thought as part of a bigger project
of describing quantum geometry in quantum information terms.Comment: 16 pages, revtex, 3 figure
Second-order amplitudes in loop quantum gravity
We explore some second-order amplitudes in loop quantum gravity. In
particular, we compute some second-order contributions to diagonal components
of the graviton propagator in the large distance limit, using the old version
of the Barrett-Crane vertex amplitude. We illustrate the geometry associated to
these terms. We find some peculiar phenomena in the large distance behavior of
these amplitudes, related with the geometry of the generalized triangulations
dual to the Feynman graphs of the corresponding group field theory. In
particular, we point out a possible further difficulty with the old
Barrett-Crane vertex: it appears to lead to flatness instead of Ricci-flatness,
at least in some situations. The observation raises the question whether this
difficulty remains with the new version of the vertex.Comment: 22 pages, 18 figure