31,244 research outputs found
Positivity in Lorentzian Barrett-Crane Models of Quantum Gravity
The Barrett-Crane models of Lorentzian quantum gravity are a family of spin
foam models based on the Lorentz group. We show that for various choices of
edge and face amplitudes, including the Perez-Rovelli normalization, the
amplitude for every triangulated closed 4-manifold is a non-negative real
number. Roughly speaking, this means that if one sums over triangulations,
there is no interference between the different triangulations. We prove
non-negativity by transforming the model into a ``dual variables'' formulation
in which the amplitude for a given triangulation is expressed as an integral
over three copies of hyperbolic space for each tetrahedron. Then we prove that,
expressed in this way, the integrand is non-negative. In addition to implying
that the amplitude is non-negative, the non-negativity of the integrand is
highly significant from the point of view of numerical computations, as it
allows statistical methods such as the Metropolis algorithm to be used for
efficient computation of expectation values of observables.Comment: 13 page
Finiteness and Dual Variables for Lorentzian Spin Foam Models
We describe here some new results concerning the Lorentzian Barrett-Crane
model, a well-known spin foam formulation of quantum gravity. Generalizing an
existing finiteness result, we provide a concise proof of finiteness of the
partition function associated to all non-degenerate triangulations of
4-manifolds and for a class of degenerate triangulations not previously shown.
This is accomplished by a suitable re-factoring and re-ordering of integration,
through which a large set of variables can be eliminated. The resulting
formulation can be interpreted as a ``dual variables'' model that uses
hyperboloid variables associated to spin foam edges in place of representation
variables associated to faces. We outline how this method may also be useful
for numerical computations, which have so far proven to be very challenging for
Lorentzian spin foam models.Comment: 15 pages, 1 figur
Temporal Correlations and Persistence in the Kinetic Ising Model: the Role of Temperature
We study the statistical properties of the sum , that is the difference of time spent positive or negative by the
spin , located at a given site of a -dimensional Ising model
evolving under Glauber dynamics from a random initial configuration. We
investigate the distribution of and the first-passage statistics
(persistence) of this quantity. We discuss successively the three regimes of
high temperature (), criticality (), and low temperature
(). We discuss in particular the question of the temperature
dependence of the persistence exponent , as well as that of the
spectrum of exponents , in the low temperature phase. The
probability that the temporal mean was always larger than the
equilibrium magnetization is found to decay as . This
yields a numerical determination of the persistence exponent in the
whole low temperature phase, in two dimensions, and above the roughening
transition, in the low-temperature phase of the three-dimensional Ising model.Comment: 21 pages, 11 PostScript figures included (1 color figure
3+1 spinfoam model of quantum gravity with spacelike and timelike components
We present a spinfoam formulation of Lorentzian quantum General Relativity.
The theory is based on a simple generalization of an Euclidean model defined in
terms of a field theory over a group. The model is an extension of a recently
introduced Lorentzian model, in which both timelike and spacelike components
are included. The spinfoams in the model, corresponding to quantized
4-geometries, carry a natural non-perturbative local causal structure induced
by the geometry of the algebra of the internal gauge (sl(2,C)). Amplitudes can
be expressed as integrals over the spacelike unit-vectors hyperboloid in
Minkowski space, or the imaginary Lobachevskian space.Comment: 16 pages, 1 figur
Virial theorem for rotating self-gravitating Brownian particles and two-dimensional point vortices
We derive the proper form of Virial theorem for a system of rotating
self-gravitating Brownian particles. We show that, in the two-dimensional case,
it takes a very simple form that can be used to obtain general results about
the dynamics of the system without being required to solve the
Smoluchowski-Poisson system explicitly. We also develop the analogy between
self-gravitating systems and two-dimensional point vortices and derive a
Virial-like relation for the vortex system
A signature of quantum gravity at the source of the seeds of cosmic structure?
This article reviews a recent work by a couple of colleagues and myself about
the shortcomings of the standard explanations of the quantum origin of cosmic
structure in the inflationary scenario, and a proposal to address them. The
point it that in the usual accounts the inhomogeneity and anisotropy of our
universe seem to emerge from an exactly homogeneous and isotropic initial state
through processes that do not break those symmetries. We argued that some novel
aspect of physics must be called upon to able to address the problem in a fully
satisfactory way. The proposed approach is inspired on Penrose's ideas
regarding an quantum gravity induced, real and dynamical collapse of the wave
function.Comment: LateX, (jpconference macros), Prepared for the proceedings the Third
International Workshop DICE 2006, " Quantum Mechanics between decoherence and
Determinism
The Seeds of Cosmic structure as a door to New Physics
There is something missing in our understanding of the origin of the seeds of
Cosmic Structuture.
The fact that the fluctuation spectrum can be extracted from the inflationary
scenario through an analysis that involves quantum field theory in curved
space-time, and that it coincides with the observational data has lead to a
certain complacency in the community, which prevents the critical analysis of
the obscure spots in the derivation. The point is that the inhomogeneity and
anisotropy of our universe seem to emerge from an exactly homogeneous and
isotropic initial state through processes that do not break those symmetries.
This article gives a brief recount of the problems faced by the arguments based
on established physics, which comprise the point of view held by a large
majority of researchers in the field.
The conclusion is that we need some new physics to be able to fully address
the problem. The article then exposes one avenue that has been used to address
the central issue and elaborates on the degree to which, the new approach makes
different predictions from the standard analyses.
The approach is inspired on Penrose's proposals that Quantum Gravity might
lead to a real, dynamical collapse of the wave function, a process that we
argue has the properties needed to extract us from the theoretical impasse
described above.Comment: Prepared for the proceedings of the conference NEBXII " Recent
Developments in Gravity", Napfio Grece June 2006. LateX, 15 page
Spin foam model for Lorentzian General Relativity
We present a spin foam formulation of Lorentzian quantum General Relativity.
The theory is based on a simple generalization of an Euclidean model defined in
terms of a field theory over a group. Its vertex amplitude turns out to be the
one recently introduced by Barrett and Crane. As in the case of its Euclidean
relatives, the model fully implements the desired sum over 2-complexes which
encodes the local degrees of freedom of the theory.Comment: 8 pages, 1 figur
Renormalization of tensor-network states
We have discussed the tensor-network representation of classical statistical
or interacting quantum lattice models, and given a comprehensive introduction
to the numerical methods we recently proposed for studying the tensor-network
states/models in two dimensions. A second renormalization scheme is introduced
to take into account the environment contribution in the calculation of the
partition function of classical tensor network models or the expectation values
of quantum tensor network states. It improves significantly the accuracy of the
coarse grained tensor renormalization group method. In the study of the quantum
tensor-network states, we point out that the renormalization effect of the
environment can be efficiently and accurately described by the bond vector.
This, combined with the imaginary time evolution of the wavefunction, provides
an accurate projection method to determine the tensor-network wavfunction. It
reduces significantly the truncation error and enable a tensor-network state
with a large bond dimension, which is difficult to be accessed by other
methods, to be accurately determined.Comment: 18 pages 23 figures, minor changes, references adde
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