837 research outputs found
Scaling behaviour in random non-commutative geometries
Random non-commutative geometries are a novel approach to taking a
non-perturbative path integral over geometries. They were introduced in
arxiv.org/abs/1510.01377, where a first examination was performed. During this
examination we found that some geometries show indications of a phase
transition. In this article we explore this phase transition further for
geometries of type , , and . We determine the pseudo
critical points of these geometries and explore how some of the observables
scale with the system size. We also undertake first steps towards understanding
the critical behaviour through correlations and in determining critical
exponents of the system.Comment: 16 pages, 16 figures (v2: updated after review
Towards a Definition of Locality in a Manifoldlike Causal Set
It is a common misconception that spacetime discreteness necessarily implies
a violation of local Lorentz invariance. In fact, in the causal set approach to
quantum gravity, Lorentz invariance follows from the specific implementation of
the discreteness hypothesis. However, this comes at the cost of locality. In
particular, it is difficult to define a "local" region in a manifoldlike causal
set, i.e., one that corresponds to an approximately flat spacetime region.
Following up on suggestions from previous work, we bridge this lacuna by
proposing a definition of locality based on the abundance of m-element
order-intervals as a function of m in a causal set. We obtain analytic
expressions for the expectation value of this function for an ensemble of
causal set that faithfully embeds into an Alexandrov interval in d-dimensional
Minkowski spacetime and use it to define local regions in a manifoldlike causal
set. We use this to argue that evidence of local regions is a necessary
condition for manifoldlikeness in a causal set. This in addition provides a new
continuum dimension estimator. We perform extensive simulations which support
our claims.Comment: 35 pages, 17 figure
Causal set d'Alembertians for various dimensions
We propose, for dimension d, a discrete Lorentz invariant operator on scalar
fields that approximates the Minkowski spacetime scalar d'Alembertian. For each
dimension, this gives rise to a scalar curvature estimator for causal sets, and
thence to a proposal for a causal set action.Comment: 14 pages, 1 figure, published in Class. Quantum Grav (text and figure
were updated to agree with the published version
Finite Size Scaling in 2d Causal Set Quantum Gravity
We study the -dependent behaviour of causal set quantum
gravity. This theory is known to exhibit a phase transition as the analytic
continuation parameter , akin to an inverse temperature, is varied.
Using a scaling analysis we find that the asymptotic regime is reached at
relatively small values of . Focussing on the causal set
action , we find that scales like where
the scaling exponent takes different values on either side of the phase
transition. For we find that which is consistent with
our analytic predictions for a non-continuum phase in the large regime.
For we find that , consistent with a continuum phase of
constant negative curvature thus suggesting a dynamically generated
cosmological constant. Moreover, we find strong evidence that the phase
transition is first order. Our results strongly suggest that the asymptotic
regime is reached in causal set quantum gravity for .Comment: 32 pages, 27 figures (v2 typos and missing reference fixed
A closed form expression for the causal set d'Alembertian
Recently a definition for a Lorentz invariant operator approximating the
d'Alembertian in d-dimensional causal set space-times has been proposed. This
operator contains several dimension-dependent constants which have been
determined for d=2,...,7. In this note we derive closed form expressions for
these constants, which are valid in all dimensions. Using these we prove that
the causal set action in any dimension can be defined through this discrete
d'Alembertian, with a dimension independent prefactor.Comment: 20 pages + 20 pages appendix, to be published in CQ
Quantum Gravity on the computer: Impressions of a workshop
Computer simulations allow us to explore non-perturbative phenomena in
physics. This has the potential to help us understand quantum gravity. Finding
a theory of quantum gravity is a hard problem, but in the last decades many
promising and intriguing approaches that utilize or might benefit from using
numerical methods were developed. These approaches are based on very different
ideas and assumptions, yet they face the common challenge to derive predictions
and compare them to data. In March 2018 we held a workshop at the Nordic
Institute for Theoretical Physics (NORDITA) in Stockholm gathering experts in
many different approaches to quantum gravity for a workshop on "Quantum gravity
on the computer". In this article we try to encapsulate some of the discussions
held and talks given during this workshop and combine them with our own
thoughts on why and how numerical approaches will play an important role in
pushing quantum gravity forward. The last section of the article is a road map
providing an outlook of the field and some intentions and goalposts that were
debated in the closing session of the workshop. We hope that it will help to
build a strong numerical community reaching beyond single approaches to combine
our efforts in the search for quantum gravity.Comment: 22 pages, 1 figure, impressions from the workshop "Quantum gravity on
the computer" at Nordita ( nordita.org/qg2018 ); v2: minor corrections,
speakers contributions to workshop more distinguished, references adde
Extrinsic curvature in two-dimensional causal dynamical triangulation
Causal dynamical triangulation (CDT) is a nonperturbative quantization of general relativity. Hořava-Lifshitz gravity, on the other hand, modifies general relativity to allow for perturbative quantization. Past work has given rise to the speculation that Hořava-Lifshitz gravity might correspond to the continuum limit of CDT. In this paper we add another piece to this puzzle by applying the CDT quantization prescription directly to Hořava-Lifshitz gravity in two dimensions. We derive the continuum Hamiltonian, and we show that it matches exactly the Hamiltonian derived from canonically quantizing the Hořava-Lifshitz action. Unlike the standard CDT case, here the introduction of a foliated lattice does not impose further restriction on the configuration space and, as a result, lattice quantization does not leave any imprint on continuum physics as expected
Development of a model educational presentation on Zendium directed towards graduating dental and dental hygiene students
Thesis (M.S.)--Boston University, Henry M. Goldman School of Graduate Dentistry, 1984 (Dental Public Health).Includes bibliographical references (leaves 58-59).Future dental professionals receive very little information on new dental products. The goal of this project was to introduce Zendium, a new dentifrice manufactured by CooperCare, Oral-B, to graduating dental studentS, post doctoral periodontic students and senior dental hygiene students. This information was presented at the dental and dental hygiene schools to fifteen (15) dental students, thirteen (13) periodontic students and eighty-one (81) dental hygiene students. Students were asked to complete two questionnaires to evaluate the appropriateness of the presentation and their reaction to Zendium. Results indicated that the students felt the presentation was appropriate in terms of the educational level, length of presentation, use of visual aids and speaker’s knowledge of the product. Their response to Zendium was mixed, with the highest acceptance of the product by senior dental hygiene students. The students had several concerns about the product, including flavor, lack of ADA approval and the need for more long-term clinical studies to be conducted in the United States. It is hoped that this information will aid CooperCare, Oral-B with their marketing strategies of Zendium to other dental professionals
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