115 research outputs found
Three dimensional Loop Quantum Gravity: towards a self-gravitating Quantum Field Theory
In a companion paper, we have emphasized the role of the Drinfeld double
DSU(2) in the context of three dimensional Riemannian Loop Quantum Gravity
coupled to massive spinless point particles. We make use of this result to
propose a model for a self-gravitating quantum field theory (massive spinless
non-causal scalar field) in three dimensional Riemannian space. We start by
constructing the Fock space of the free self-gravitating field: the vacuum is
the unique DSU(2) invariant state, one-particle states correspond to DSU(2)
unitary irreducible simple representations and any multi-particles states is
obtained as the symmetrized tensor product between simple representations. The
associated quantum field is defined by the usual requirement of covariance
under DSU(2). Then, we introduce a DSU(2)-invariant self-interacting potential
(the obtained model is a Group Field Theory) and compute explicitely the lowest
order terms (in the self-interaction coupling constant ) of the
propagator and of the three-points function. Finally, we compute the lowest
order quantum gravity corrections (in the Newton constant G) to the propagator
and to the three-points function.Comment: 36 pages, published in Class. Quant. Gra
Near-Horizon Radiation and Self-Dual Loop Quantum Gravity
We compute the near-horizon radiation of quantum black holes in the context
of self-dual loop quantum gravity. For this, we first use the unitary spinor
basis of to decompose states of Lorentzian spin foam
models into their self-dual and anti self-dual parts, and show that the reduced
density matrix obtained by tracing over one chiral component describes a
thermal state at Unruh temperature. Then, we show that the
analytically-continued dimension of the Chern-Simons Hilbert
space, which reproduces the Bekenstein-Hawking entropy in the large spin limit
in agreement with the large spin effective action, takes the form of a
partition function for states thermalized at Unruh temperature, with discrete
energy levels given by the near-horizon energy of Frodden-Gosh-Perez, and with
a degenerate ground state which is holographic and responsible for the entropy.Comment: 6+2 page
Observability and Geometry in Three dimensional quantum gravity
We consider the coupling between massive and spinning particles and three
dimensional gravity. This allows us to construct geometric operators (distances
between particles) as Dirac observables. We quantize the system a la loop
quantum gravity: we give a description of the kinematical Hilbert space and
construct the associated spin-foam model. We construct the physical disctance
operator and consider its quantization.Comment: To appear in the procedings of the Third International Symposium on
Quantum Theory and Symmetries (QTS3), September 200
Dynamics of loop quantum gravity and spin foam models in three dimensions
We present a rigorous regularization of Rovellis's generalized projection
operator in canonical 2+1 gravity. This work establishes a clear-cut connection
between loop quantum gravity and the spin foam approach in this simplified
setting. The point of view adopted here provides a new perspective to tackle
the problem of dynamics in the physically relevant
3+1 case.Comment: To appear in the procedings of the Third International Symposium on
Quantum Theory and Symmetries (QTS3), September 200
Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
Theories with higher order time derivatives generically suffer from
ghost-like instabilities, known as Ostrogradski instabilities. This fate can be
avoided by considering "degenerate" Lagrangians, whose kinetic matrix cannot be
inverted, thus leading to constraints between canonical variables and a reduced
number of physical degrees of freedom. In this work, we derive in a systematic
way the degeneracy conditions for scalar-tensor theories that depend
quadratically on second order derivatives of a scalar field. We thus obtain a
classification of all degenerate theories within this class of scalar-tensor
theories. The quartic Horndeski Lagrangian and its extension beyond Horndeski
belong to these degenerate cases. We also identify new families of
scalar-tensor theories with the intriguing property that they are degenerate
despite the nondegeneracy of the purely scalar part of their Lagrangian.Comment: 19 pages, no figur
A note on the Holst action, the time gauge, and the Barbero-Immirzi parameter
In this note, we review the canonical analysis of the Holst action in the
time gauge, with a special emphasis on the Hamiltonian equations of motion and
the fixation of the Lagrange multipliers. This enables us to identify at the
Hamiltonian level the various components of the covariant torsion tensor, which
have to be vanishing in order for the classical theory not to depend upon the
Barbero-Immirzi parameter. We also introduce a formulation of three-dimensional
gravity with an explicit phase space dependency on the Barbero-Immirzi
parameter as a potential way to investigate its fate and relevance in the
quantum theory.Comment: 22 pages. Published version. Choice of gauge at the begining of
section II.B. clarified. Published in Gen. Rel. Grav. (2013
Spin-Foam Models and the Physical Scalar Product
This paper aims at clarifying the link between Loop Quantum Gravity and
Spin-Foam models in four dimensions. Starting from the canonical framework, we
construct an operator P acting on the space of cylindrical functions
Cyl(), where is the 4-simplex graph, such that its ma- trix
elements are, up to some normalization factors, the vertex amplitude of
Spin-Foam models. The Spin-Foam models we are considering are the topological
model, the Barrett-Crane model and the Engle-Pereira-Rovelli model. The
operator P is usually called the "projector" into physical states and its
matrix elements gives the physical scalar product. Therefore, we relate the
physical scalar product of Loop Quantum Gravity to vertex amplitudes of some
Spin-Foam models. We discuss the possibility to extend the action of P to any
cylindrical functions on the space manifold.Comment: 24 page
Statistics, holography, and black hole entropy in loop quantum gravity
In loop quantum gravity the quantum states of a black hole horizon are
produced by point-like discrete quantum geometry excitations (or {\em
punctures}) labelled by spin . The excitations possibly carry other internal
degrees of freedom also, and the associated quantum states are eigenstates of
the area operator. On the other hand, the appropriately scaled area
operator is also the physical Hamiltonian associated with the
quasilocal stationary observers located at a small distance from the
horizon. Thus, the local energy is entirely accounted for by the geometric
operator .
We assume that: In a suitable vacuum state with regular energy momentum
tensor at and close to the horizon the local temperature measured by stationary
observers is the Unruh temperature and the degeneracy of `matter' states is
exponential with the area ---this is supported by
the well established results of QFT in curved spacetimes, which do not
determine but asserts an exponential behaviour. The geometric
excitations of the horizon (punctures) are indistinguishable. In the
semiclassical limit the area of the black hole horizon is large in Planck
units.
It follows that: Up to quantum corrections, matter degrees of freedom
saturate the holographic bound, {\em viz.} . Up to quantum
corrections, the statistical black hole entropy coincides with
Bekenstein-Hawking entropy . The number of horizon
punctures goes like , i.e the number of punctures
remains large in the semiclassical limit. Fluctuations of the horizon area
are small while fluctuations of the area of an individual puncture are large. A
precise notion of local conformal invariance of the thermal state is recovered
in the limit where the near horizon geometry becomes Rindler
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