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($\Gamma$), where $\Gamma$ 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

Canonical Analysis of Algebraic String Actions

We investigate the canonical aspects of the algebraic first order formulation of strings introduced two decades ago by Balachandran and collaborators. We slightly enlarge the Lagrangian framework and show the existence of a self-dual formulation and of an Immirzi-type parameter reminiscent of four-dimensional first order gravity. We perform a full Hamiltonian analysis of the self-dual case: we extract the first class constraints and construct the Dirac bracket associated to the second class constraints. The first class constraints contain the diffeomorphisms algebra on the world-sheet, and the coordinates are shown to be non-commutative with respect to the Dirac bracket. The Hamilton equations in a particular gauge are shown to reproduce the wave equation for the string coordinates. In the general, non-self-dual case, we also explicit the first class constraints of the system and show that, unlike the self-dual formulation, the theory admits an extra propagating degree of freedom than the two degrees of freedom of conventional string theory. This prevents the general algebraic string from being strictly equivalent to the Nambu-Goto string.Comment: Title changed. Presentation improved. Typos correcte

A Lorentz-Covariant Connection for Canonical Gravity

We construct a Lorentz-covariant connection in the context of first order canonical gravity with non-vanishing Barbero-Immirzi parameter. To do so, we start with the phase space formulation derived from the canonical analysis of the Holst action in which the second class constraints have been solved explicitly. This allows us to avoid the use of Dirac brackets. In this context, we show that there is a "unique" Lorentz-covariant connection which is commutative in the sense of the Poisson bracket, and which furthermore agrees with the connection found by Alexandrov using the Dirac bracket. This result opens a new way toward the understanding of Lorentz-covariant loop quantum gravity

Pectin-based bioinks for 3D models of neural tissue produced by a pH-controlled kinetics

Introduction:In the view of 3D-bioprinting with cell models representative of neural cells, we produced inks to mimic the basic viscoelastic properties of brain tissue. Moving from the concept that rheology provides useful information to predict ink printability, this study improves and expands the potential of the previously published 3D-reactive printing approach by introducing pH as a key parameter to be controlled, together with printing time. Methods:The viscoelastic properties, printability, and microstructure of pectin gels crosslinked with CaCO3 were investigated and their composition was optimized (i.e., by including cell culture medium, HEPES buffer, and collagen). Different cell models representative of the major brain cell populations (i.e., neurons, astrocytes, microglial cells, and oligodendrocytes) were considered. Results and Discussion:The outcomes of this study propose a highly controllable method to optimize the printability of internally crosslinked polysaccharides, without the need for additives or post-printing treatments. By introducing pH as a further parameter to be controlled, it is possible to have multiple (pH-dependent) crosslinking kinetics, without varying hydrogel composition. In addition, the results indicate that not only cells survive and proliferate following 3D-bioprinting, but they can also interact and reorganize hydrogel microstructure. Taken together, the results suggest that pectin-based hydrogels could be successfully applied for neural cell culture

Hep3Gel: A Shape-Shifting Extracellular Matrix-Based, Three-Dimensional Liver Model Adaptable to Different Culture Systems

Drug-induced hepatotoxicity is a leading cause of clinical trial withdrawal. Therefore, in vitro modeling the hepatic behavior and functionalities is not only crucial to better understand physiological and pathological processes but also to support drug development with reliable high-throughput platforms. Different physiological and pathological models are currently under development and are commonly implemented both within platforms for standard 2D cultures and within tailor-made chambers. This paper introduces Hep3Gel: a hybrid alginate-extracellular matrix (ECM) hydrogel to produce 3D in vitro models of the liver, aiming to reproduce the hepatic chemomechanical niche, with the possibility of adapting its shape to different manufacturing techniques. The ECM, extracted and powdered from porcine livers by a specifically set-up procedure, preserved its crucial biological macromolecules and was embedded within alginate hydrogels prior to crosslinking. The viscoelastic behavior of Hep3Gel was tuned, reproducing the properties of a physiological organ, according to the available knowledge about hepatic biomechanics. By finely tuning the crosslinking kinetics of Hep3Gel, its dualistic nature can be exploited either by self-spreading or adapting its shape to different culture supports or retaining the imposed fiber shape during an extrusion-based 3D-bioprinting process, thus being a shape-shifter hydrogel. The self-spreading ability of Hep3Gel was characterized by combining empirical and numerical procedures, while its use as a bioink was experimentally characterized through rheological a priori printability evaluations and 3D printing tests. The effect of the addition of the ECM was evident after 4 days, doubling the survival rate of cells embedded within control hydrogels. This study represents a proof of concept of the applicability of Hep3Gel as a tool to develop 3D in vitro models of the liver

No title available

Dans cette thèse, nous avons étudié quelques aspects fondamentaux de la gravitation quantique à boucles (Loop Quantum Gravity ou LQG). Tout d'abord, nous avons discuté le choix de la représentation polymère dans ce programme de quantification de la relativité générale. Pour cela, nous avons considéré la corde bosonique comme modèle-jouet sur lequel on peut tester les méthodes de quantification de la LQG. Dans cette optique, nous avons introduit et étudié une formulation originale de la corde bosonique, dite corde algébrique. Ensuite, nous nous sommes intéressé au problème important du choix de la jauge temporelle en LQG. Ce choix permet de passer d'un groupe de jauge non-compact (le groupe de Lorentz) à un groupe de jauge compact (le groupe des rotations) et ainsi d'obtenir un spectre discret des opérateurs de géométrie. Nous avons montré qu'il est possible de ne pas faire le choix de la jauge temporelle, de pouvoir quantifier malgré tout la théorie et de retrouver un spectre discret des opérateurs de géométrie même avec un groupe de jauge non-compact. Enfin, nous nous sommes attaché à comprendre le lien entre les approches canonique et covariante afin de tester la validité du nouveau modèle de mousse de spins introduit par Engle, Peireira, Rovelli et Livine (EPRL).No summary availabl

Covariant and Canonical Quantum Gravity

Nel lavoro di ricerca per la tesi si è mirato a chiarire il collegamento tra i modelli di Spin Foam e la teoria della Gravità Quantistica a Loop (LQG). La LQG consiste nel considerare la relatività generale (GR) senza materia (per adesso), cioè puro campo gravitazionale, darne una formulazione hamiltoniana e quantizzare il sistema hamiltoniano ottenuto promuovendo le variabili canoniche a operatori con le corrette regole di commutazione, costruendo lo spazio di Hilbert con una struttura di prodotto scalare, ... La LQG è un tentativo di comprendere quali caratteristiche deve avere una teoria coerente che parta dai principi fondamentali della meccanica quantistica e della GR. Attualmente, la LQG non è completa: una delle principali questioni aperte, se non la principale, è quella di trovare le soluzioni della versione quantistica dell'ultimo vincolo della formulazione canonica della GR: il cosiddetto vincolo scalare. Risolvere questo problema significa anche poter trovare il prodotto scalare nello spazio di Hilbert della teoria e quindi poter calcolare, almeno in linea di principio, le ampiezze di transizione tra coppie di stati. I modelli di Spin Foam sono un tentativo di costruire una versione quantistica della GR in maniera covariante utilizzando gli integrali sui cammini di Feymann. Questi ultimi, come è ben noto, forniscono direttamente le ampiezze di transizione tra coppie di stati facendo una “somma” su “tutte” le possibili “evoluzioni” dallo stato iniziale a quello finale di una “determinata quantità” associata ad ogni “evoluzione”. Il problema centrale di questo approccio alla gravità quantistica è quello di chiarire per esempio il significato della parola “somma” usata precedentemente (cioè definire la misura di integrazione sui cammini), della parole “tutte” (cioè capire su quale insieme di cammini integrare), di chiarire qual è di preciso quella “determinata quantità” associata ad ogni cammino. Bisogna capire inoltre quali sono gli stati tra i quali calcolare le ampiezze di transizione in gravità quantistica. Ogni modello di Spin Foam dà delle proposte di risposta a queste domande. Essi utilizzano come stati iniziali e finali i cosiddetti spin network, che sono proprio gli stati che costituiscono la base dello spazio di Hilbert costruito in LQG. Gli spin network sono oggetti discreti e, sostanzialmente, una conseguenza di ciò è che l'integrale sui cammini nei modelli di Spin Foam diventa una somma discreta. Nel lavoro di ricerca per la tesi si sono presi in esame alcuni modelli di Spin Foam e si è cercato il prodotto scalare nello spazio di Hilbert della LQG che fornisce ampiezze di transizione uguali a quelle del modello di Spin Foam di volta in volta considerato. Un lavoro analogo era stato già fatto nelle 2+1 dimensioni, dove la gravità è una teoria topologica, quindi molto più semplice rispetto alla quella in 3+1 dimensioni. Risolvere questo problema significherebbe fare un passo avanti per poter capire se il prodotto scalare così trovato fornisce le soluzioni del vincolo scalare della LQG e, in caso di risposta affermativa, aver sostanzialmente completato il programma di quantizzazione canonica della gravità, lanciato da Dirac negli anni '30. Inoltre, in questo caso, si avrebbe la dimostrazione che il modello di Spin Foam considerato è equivalente alla LQG, cioè si avrebbe una versione covariante della gravità quantistica equivalente alla versione canonica. Nel lavoro di ricerca svolto si è trovata una formula per il prodotto scalare che si cercava per quanto riguarda la cosiddetta teoria BF, il modello Barrett-Crane, il modello Engle-Pereira-Rovelli (EPR) e i modelli Freidel-Krasnov. Tale formula è stata trovata nel caso di una transizione tra stati semplici, la quale è probabilmente il mattoncino fondamentale per le ampiezze di transizione tra una qualsiasi coppia di stati. Non è ancora chiaro per bene se uno di questi prodotti scalari fornisce le soluzioni al vincolo scalare. La formula trovata potrebbe essere utile per calcolare il limite classico e semiclassico del modello EPR, l'attuale candidato principe per la gravità quantistica covariante

3D-reactive printing of engineered alginate inks

Alginate is a common component of bioinks due to its well-described ionic crosslinking mechanism and its tunable viscoelastic properties. The extrusion-based 3D-printing of alginate inks requires additives, such as gelatin and Pluronic, pre or post- printing crosslinking processes and/or coextrusion with crosslinkers. In this work, we aim to provide a diffent printing approach of alginate-based inks, introducing the 3D-reactive printing. Indeed, the control over the crosslinking kinetics and the printing time allowed printing different inks while maintaining unaltered their final composition to identify a suitable formulation in terms of printability. Alginate solutions were crosslinked with insoluble calcium salts (CaCO3) inducing dynamic modification of their microstructure and viscoelastic properties in time. The monitoring of fibers printability and internal microstructure, at the different time points of the ink gelation, was performed by means of a well-defined set of rheological tests to engineer a priori inks properties for the a posteriori 3D-printing process. This new perspective allowed 3D reactive printing of alginate fibers with predermined properties, without involving post-extrusion crosslinking steps and additives