Counting surface states in the loop quantum gravity

We adopt the point of view that (Riemannian) classical and (loop-based) quantum descriptions of geometry are macro- and micro-descriptions in the usual statistical mechanical sense. This gives rise to the notion of geometrical entropy, which is defined as the logarithm of the number of different quantum states which correspond to one and the same classical geometry configuration (macro-state). We apply this idea to gravitational degrees of freedom induced on an arbitrarily chosen in space 2-dimensional surface. Considering an `ensemble' of particularly simple quantum states, we show that the geometrical entropy $S(A)$ corresponding to a macro-state specified by a total area $A$ of the surface is proportional to the area $S(A)=\alpha A$, with $\alpha$ being approximately equal to $1/16\pi l_p^2$. The result holds both for case of open and closed surfaces. We discuss briefly physical motivations for our choice of the ensemble of quantum states.Comment: This paper is a substantially modified version of the paper `The Bekenstein bound and non-perturbative quantum gravity'. Although the main result (i.e. the result of calculation of the number of quantum states that correspond to one and the same area of 2-d surface) remains unchanged, it is presented now from a different point of view. The new version contains a discussion both of the case of open and closed surfaces, and a discussion of a possibility to generalize the result obtained considering arbitrary surface quantum states. LaTeX, 21 pages, 6 figures adde

Group Field Theory: An overview

We give a brief overview of the properties of a higher dimensional generalization of matrix model which arises naturally in the context of a background independent approach to quantum gravity, the so called group field theory. We show that this theory leads to a natural proposal for the physical scalar product of quantum gravity. We also show in which sense this theory provides a third quantization point of view on quantum gravity.Comment: 10 page

Gauging kinematical and internal symmetry groups for extended systems: the Galilean one-time and two-times harmonic oscillators

The possible external couplings of an extended non-relativistic classical system are characterized by gauging its maximal dynamical symmetry group at the center-of-mass. The Galilean one-time and two-times harmonic oscillators are exploited as models. The following remarkable results are then obtained: 1) a peculiar form of interaction of the system as a whole with the external gauge fields; 2) a modification of the dynamical part of the symmetry transformations, which is needed to take into account the alteration of the dynamics itself, induced by the {\it gauge} fields. In particular, the Yang-Mills fields associated to the internal rotations have the effect of modifying the time derivative of the internal variables in a scheme of minimal coupling (introduction of an internal covariant derivative); 3) given their dynamical effect, the Yang-Mills fields associated to the internal rotations apparently define a sort of Galilean spin connection, while the Yang-Mills fields associated to the quadrupole momentum and to the internal energy have the effect of introducing a sort of dynamically induced internal metric in the relative space.Comment: 32 pages, LaTex using the IOP preprint macro package (ioplppt.sty available at: http://www.iop.org/). The file is available at: http://www.fis.unipr.it/papers/1995.html The file is a uuencoded tar gzip file with the IOP preprint style include

Local dark matter searches with LISA

The drag-free satellites of LISA will maintain the test masses in geodesic motion over many years with residual accelerations at unprecedented small levels and time delay interferometry (TDI) will keep track of their differential positions at level of picometers. This may allow investigations of fine details of the gravitational field in the Solar System previously inaccessible. In this spirit, we present the concept of a method to measure directly the gravitational effect of the density of diffuse Local Dark Matter (LDM) with a constellation of a few drag-free satellites, by exploiting how peculiarly it would affect their relative motion. Using as test bed an idealized LISA with rigid arms, we find that the separation in time between the test masses is uniquely perturbed by the LDM, so that they acquire a differential breathing mode. Such a LDM signal is related to the LDM density within the orbits and has characteristic spectral components, with amplitudes increasing in time, at various frequencies of the dynamics of the constellation. This is the relevant result, in that the LDM signal is brought to non-zero frequencies.Comment: 8 pages, 1 figure; v2: minor changes to match the version in press on Classical and Quantum Gravity (special issue for the 7th International LISA Symposium proceedings

Modulation of LISA free-fall orbits due to the Earth-Moon system

We calculate the effect of the Earth-Moon (EM) system on the free-fall motion of LISA test masses. We show that the periodic gravitational pulling of the EM system induces a resonance with fundamental frequency 1 yr^-1 and a series of periodic perturbations with frequencies equal to integer harmonics of the synodic month (9.92 10^-7 Hz). We then evaluate the effects of these perturbations (up to the 6th harmonics) on the relative motions between each test masses couple, finding that they range between 3mm and 10pm for the 2nd and 6th harmonic, respectively. If we take the LISA sensitivity curve, as extrapolated down to 10^-6 Hz, we obtain that a few harmonics of the EM system can be detected in the Doppler data collected by the LISA space mission. This suggests that the EM system gravitational near field could provide an absolute calibration for the LISA sensitivity at very low frequencies.Comment: 15 pages, 5 figure

Implementation of an enhanced recovery program after bariatric surgery: Clinical and cost-effectiveness analysis

Enhanced recovery after surgery (ERAS) programs are perioperative evidence-based interventions that have the purpose of making the perioperative pathway more efficient in safeguarding patient safety and quality of care. Recently, several ERAS components have been introduced in the setting of bariatric surgery (Enhanced Recovery After Bariatric Surgery, ERABS). The aim of the present study was to evaluate clinical efficiency and cost-effectiveness of the implementation of an ERABS program. It was a retrospective case-control study comparing a group of adult obese (body mass index >40) patients treated according to the ERABS protocol (2014-2015) with a historical control group that received standard care (2013-2014) in the General and Emergency Surgery Department, Arcispedale S. Maria Nuova Hospital, Reggio Emilia, Italy. Data on the occurrence of complications, mortality, re-admissions and re-operations were extracted retrospectively from medical case notes and emergency patient admission lists. Length of hospital stay was significantly different between the two cohort patients. In the control group, the mean length of stay was 12.6±10.9 days, whereas in the ERABS cohort it was 7.1±2.9 days (p=0.02). During hospital stay, seven patients in the control group developed surgical complications, including one patient with major complications, whereas in the ERABS group three patients developed minor complications. Economic analysis revealed a different cost distribution between the two groups. On the whole, there were significant savings for almost all the variables taken into consideration, mainly driven by exclusion of using intensive care unit, which is by far more expensive than the average cost of post-anesthesia care unit. Our study confirmed the implementation of an ERABS protocol to have shortened hospital stay and was cost-saving while safeguarding patient safety

The York map as a Shanmugadhasan canonical transformation in tetrad gravity and the role of non-inertial frames in the geometrical view of the gravitational field

A new parametrization of the 3-metric allows to find explicitly a York map in canonical ADM tetrad gravity, the two pairs of physical tidal degrees of freedom and 14 gauge variables. These gauge quantities (generalized inertial effects) are all configurational except the trace ${}^3K(\tau ,\vec \sigma)$ of the extrinsic curvature of the instantaneous 3-spaces $\Sigma_{\tau}$ (clock synchronization convention) of a non-inertial frame. The Dirac hamiltonian is the sum of the weak ADM energy $E_{ADM} = \int d^3\sigma {\cal E}_{ADM}(\tau ,\vec \sigma)$ (whose density is coordinate-dependent due to the inertial potentials) and of the first-class constraints. Then: i) The explicit form of the Hamilton equations for the two tidal degrees of freedom in an arbitrary gauge: a deterministic evolution can be defined only in a completely fixed gauge, i.e. in a non-inertial frame with its pattern of inertial forces. ii) A general solution of the super-momentum constraints, which shows the existence of a generalized Gribov ambiguity associated to the 3-diffeomorphism gauge group. It influences: a) the explicit form of the weak ADM energy and of the super-momentum constraint; b) the determination of the shift functions and then of the lapse one. iii) The dependence of the Hamilton equations for the two pairs of dynamical gravitational degrees of freedom (the generalized tidal effects) and for the matter, written in a completely fixed 3-orthogonal Schwinger time gauge, upon the gauge variable ${}^3K(\tau ,\vec \sigma)$, determining the convention of clock synchronization. Therefore it should be possible (for instance in the weak field limit but with relativistic motion) to try to check whether in Einstein's theory the {\it dark matter} is a gauge relativistic inertial effect induced by ${}^3K(\tau ,\vec \sigma)$.Comment: 90 page

Spacetime as a Feynman diagram: the connection formulation

Spin foam models are the path integral counterparts to loop quantized canonical theories. In the last few years several spin foam models of gravity have been proposed, most of which live on finite simplicial lattice spacetime. The lattice truncates the presumably infinite set of gravitational degrees of freedom down to a finite set. Models that can accomodate an infinite set of degrees of freedom and that are independent of any background simplicial structure, or indeed any a priori spacetime topology, can be obtained from the lattice models by summing them over all lattice spacetimes. Here we show that this sum can be realized as the sum over Feynman diagrams of a quantum field theory living on a suitable group manifold, with each Feynman diagram defining a particular lattice spacetime. We give an explicit formula for the action of the field theory corresponding to any given spin foam model in a wide class which includes several gravity models. Such a field theory was recently found for a particular gravity model [De Pietri et al, hep-th/9907154]. Our work generalizes this result as well as Boulatov's and Ooguri's models of three and four dimensional topological field theories, and ultimately the old matrix models of two dimensional systems with dynamical topology. A first version of our result has appeared in a companion paper [gr-qc\0002083]: here we present a new and more detailed derivation based on the connection formulation of the spin foam models.Comment: 32 pages, 2 figure

apeNEXT: A multi-TFlops Computer for Simulations in Lattice Gauge Theory

We present the APE (Array Processor Experiment) project for the development of dedicated parallel computers for numerical simulations in lattice gauge theories. While APEmille is a production machine in today's physics simulations at various sites in Europe, a new machine, apeNEXT, is currently being developed to provide multi-Tflops computing performance. Like previous APE machines, the new supercomputer is largely custom designed and specifically optimized for simulations of Lattice QCD.Comment: Poster at the XXIII Physics in Collisions Conference (PIC03), Zeuthen, Germany, June 2003, 3 pages, Latex. PSN FRAP15. Replaced for adding forgotten autho

Colored Group Field Theory

Group field theories are higher dimensional generalizations of matrix models. Their Feynman graphs are fat and in addition to vertices, edges and faces, they also contain higher dimensional cells, called bubbles. In this paper, we propose a new, fermionic Group Field Theory, posessing a color symmetry, and take the first steps in a systematic study of the topological properties of its graphs. Unlike its bosonic counterpart, the bubbles of the Feynman graphs of this theory are well defined and readily identified. We prove that this graphs are combinatorial cellular complexes. We define and study the cellular homology of this graphs. Furthermore we define a homotopy transformation appropriate to this graphs. Finally, the amplitude of the Feynman graphs is shown to be related to the fundamental group of the cellular complex