15,983 research outputs found
On the regularization ambiguities in loop quantum gravity
One of the main achievements of LQG is the consistent quantization of the
Wheeler-DeWitt equation which is free of UV problems. However, ambiguities
associated to the intermediate regularization procedure lead to an apparently
infinite set of possible theories. The absence of an UV problem is intimately
linked with the ambiguities arising in the quantum theory. Among these
ambiguities there is the one associated to the SU(2) unitary rep. used in the
diffeomorphism covariant pointsplitting regularization of nonlinear funct. of
the connection. This ambiguity is labelled by a halfinteger m and, here, it is
referred to as the m-ambiguity. The aim of this paper is to investigate the
important implications of this ambiguity./ We first study 2+1 gravity quantized
in canonical LQG. Only when the regularization of the quantum constraints is
performed in terms of the fundamental rep. of the gauge group one obtains the
usual TQFT. In all other cases unphysical local degrees of freedom arise at the
level of the regulated theory that conspire against the existence of the
continuum limit. This shows that there is a clear cut choice in the
quantization of the constraints in 2+1 LQG./ We then analyze the effects of the
ambiguity in 3+1 gravity exhibiting the existence of spurious solutions for
higher unit. rep. quantizations of the Hamiltonian constraint. Although the
analysis is not complete in D=3+1--due to the difficulties associated to the
definition of the physical inner product--it provides evidence supporting the
definitions quantum dynamics of loop quantum gravity in terms of the
fundamental representation of the gauge group as the only consistent
possibilities. If the gauge group is SO(3) we find physical solutions
associated to spin-two local excitations.Comment: 21 page
Parameters estimation for spatio-temporal maximum entropy distributions: application to neural spike trains
We propose a numerical method to learn Maximum Entropy (MaxEnt) distributions
with spatio-temporal constraints from experimental spike trains. This is an
extension of two papers [10] and [4] who proposed the estimation of parameters
where only spatial constraints were taken into account. The extension we
propose allows to properly handle memory effects in spike statistics, for large
sized neural networks.Comment: 34 pages, 33 figure
Loop Quantum Gravity: Four Recent Advances and a Dozen Frequently Asked Questions
As per organizers' request, my talk at the 11th Marcel Grossmann Conference
consisted of two parts. In the first, I illustrated recent advances in loop
quantum gravity through examples. In the second, I presented an overall
assessment of the status of the program by addressing some frequently asked
questions. This account is addressed primarily to researchers outside the loop
quantum gravity community.Comment: 21 pages, to appear in the Proceedings of the 11th Marcel Grossmann
Conferenc
A statistical mechanics framework for static granular matter
The physical properties of granular materials have been extensively studied
in recent years. So far, however, there exists no theoretical framework which
can explain the observations in a unified manner beyond the phenomenological
jamming diagram [1]. This work focuses on the case of static granular matter,
where we have constructed a statistical ensemble [2] which mirrors equilibrium
statistical mechanics. This ensemble, which is based on the conservation
properties of the stress tensor, is distinct from the original Edwards ensemble
and applies to packings of deformable grains. We combine it with a field
theoretical analysis of the packings, where the field is the Airy stress
function derived from the force and torque balance conditions. In this
framework, Point J characterized by a diverging stiffness of the pressure
fluctuations. Separately, we present a phenomenological mean-field theory of
the jamming transition, which incorporates the mean contact number as a
variable. We link both approaches in the context of the marginal rigidity
picture proposed by [3, 4].Comment: 21 pages, 15 figure
Hunter-gatherers in a howling wilderness: Neoliberal capitalism as a language that speaks itself
The 'self-referential' character of evolutionary process noted by Goldenfeld and Woese (2010) can be restated in the context of a generalized Darwinian theory applied to economic process through a 'language' model: The underlying inherited and learned culture of the firm, the short-time cognitive response of the firm to patterns of threat and opportunity that is sculpted by that culture, and the embedding socioeconomic environment, are represented as interacting information sources constrained by the asymptotic limit theorems of information theory. If unregulated, the larger, compound, source that characterizes high probability evolutionary paths of this composite then becomes, literally, a self-dynamic language that speaks itself. Such a structure is, for those enmeshed in it, more akin to a primitive hunter-gatherer society at the mercy of internal ecological dynamics than to, say, a neolithic agricultural community in which a highly ordered, deliberately adapted, ecosystem is consciously farmed so as to match its productivity to human needs
Background Independent Quantum Gravity: A Status Report
The goal of this article is to present an introduction to loop quantum
gravity -a background independent, non-perturbative approach to the problem of
unification of general relativity and quantum physics, based on a quantum
theory of geometry. Our presentation is pedagogical. Thus, in addition to
providing a bird's eye view of the present status of the subject, the article
should also serve as a vehicle to enter the field and explore it in detail. To
aid non-experts, very little is assumed beyond elements of general relativity,
gauge theories and quantum field theory. While the article is essentially
self-contained, the emphasis is on communicating the underlying ideas and the
significance of results rather than on presenting systematic derivations and
detailed proofs. (These can be found in the listed references.) The subject can
be approached in different ways. We have chosen one which is deeply rooted in
well established physics and also has sufficient mathematical precision to
ensure that there are no hidden infinities. In order to keep the article to a
reasonable size, and to avoid overwhelming non-experts, we have had to leave
out several interesting topics, results and viewpoints; this is meant to be an
introduction to the subject rather than an exhaustive review of it.Comment: 125 pages, 5 figures (eps format), the final version published in CQ
The Statistical Physics of Athermal Materials
At the core of equilibrium statistical mechanics lies the notion of
statistical ensembles: a collection of microstates, each occurring with a given
a priori probability that depends only on a few macroscopic parameters such as
temperature, pressure, volume, and energy. In this review article, we discuss
recent advances in establishing statistical ensembles for athermal materials.
The broad class of granular and particulate materials is immune from the
effects of thermal fluctuations because the constituents are macroscopic. In
addition, interactions between grains are frictional and dissipative, which
invalidates the fundamental postulates of equilibrium statistical mechanics.
However, granular materials exhibit distributions of microscopic quantities
that are reproducible and often depend on only a few macroscopic parameters. We
explore the history of statistical ensemble ideas in the context of granular
materials, clarify the nature of such ensembles and their foundational
principles, highlight advances in testing key ideas, and discuss applications
of ensembles to analyze the collective behavior of granular materials
Gibbs and Quantum Discrete Spaces
Gibbs measure is one of the central objects of the modern probability,
mathematical statistical physics and euclidean quantum field theory. Here we
define and study its natural generalization for the case when the space, where
the random field is defined is itself random. Moreover, this randomness is not
given apriori and independently of the configuration, but rather they depend on
each other, and both are given by Gibbs procedure; We call the resulting object
a Gibbs family because it parametrizes Gibbs fields on different graphs in the
support of the distribution. We study also quantum (KMS) analog of Gibbs
families. Various applications to discrete quantum gravity are given.Comment: 37 pages, 2 figure
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