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Matteo Smerlak

Publications and source records attributed to Matteo Smerlak.

46 records · Page 3Linked to original sources
arXiv2011

In quantum gravity, summing is refining

In perturbative QED, the approximation is improved by summing more Feynman graphs; in non-perturbative QCD, by refining the lattice. Here we observe that in quantum gravity the two procedures may well be the same. We outline the combinatorial structure of spinfoam quantum gravity, define the continuum limit, and show that under general conditions refining foams is the same as summing over them. The conditions bear on the cylindrical consistency of the spinfoam amplitudes and on the presence of appropriate combinatorial factors, related to the implementation of diffeomorphisms invariance. Intuitively, the sites of the lattice are points of space: these are themselves quanta of the gravitational field, and thus a lattice discretization is also a Feynman history of quanta.

gr-qc↗
arXiv2011

Bubble divergences: sorting out topology from cell structure

We conclude our analysis of bubble divergences in the flat spinfoam model. In [arXiv:1008.1476] we showed that the divergence degree of an arbitrary two-complex Gamma can be evaluated exactly by means of twisted cohomology. Here, we specialize this result to the case where Gamma is the two-skeleton of the cell decomposition of a pseudomanifold, and sharpen it with a careful analysis of the cellular and topological structures involved. Moreover, we explain in detail how this approach reproduces all the previous powercounting results for the Boulatov-Ooguri (colored) tensor models, and sheds light on algebraic-topological aspects of Gurau's 1/N expansion.

gr-qc↗
arXiv2011

Thermal time and the Tolman-Ehrenfest effect: temperature as the "speed of time"

The notion of thermal time has been introduced as a possible basis for a fully general-relativistic thermodynamics. Here we study this notion in the restricted context of stationary spacetimes. We show that the Tolman-Ehrenfest effect (in a stationary gravitational field, temperature is not constant in space at thermal equilibrium) can be derived very simply by applying the equivalence principle to a key property of thermal time: at equilibrium, temperature is the rate of thermal time with respect to proper time - the `speed of (thermal) time'. Unlike other published derivations of the Tolman-Ehrenfest relation, this one is free from any further dynamical assumption, thereby illustrating the physical import of the notion of thermal time.

gr-qc↗
arXiv2010

A blackbody is not a blackbox

We discuss carefully the blackbody approximation, stressing what it is (a limit case of radiative transfer), and what it is not (the assumption that the body is perfectly absorbing, i.e. black). Furthermore, we derive the Planck spectrum without enclosing the field in a box, as is done in most textbooks. Athough convenient, this trick conceals the nature of the idealization expressed in the concept of a blackbody: first, the most obvious examples of approximate blackbodies, stars, are definitely not enclosed in boxes; second, the Planck spectrum is continuous, while the stationary modes of radiation in a box are discrete. Our derivation, although technically less elementary, is conceptually more consistent, and brings the opportunity to introduce to students the important concept of local density of states, via the resolvent formalism.

physics.class-ph↗
arXiv2010

Bubble divergences from twisted cohomology

We consider a class of lattice topological field theories, among which are the weak-coupling limit of 2d Yang-Mills theory and 3d Riemannian quantum gravity, whose dynamical variables are flat discrete connections with compact structure group on a cell 2-complex. In these models, it is known that the path integral measure is ill-defined because of a phenomenon known as `bubble divergences'. In this paper, we extend recent results of the authors to the cases where these divergences cannot be understood in terms of cellular cohomology. We introduce in its place the relevant {\it twisted} cohomology, and use it to compute the divergence degree of the partition function. We also relate its dominant part to the Reidemeister torsion of the complex, thereby generalizing previous results of Barrett and Naish-Guzman. The main limitation to our approach is the presence of singularities in the representation variety of the fundamental group of the complex; we illustrate this issue in the well-known case of two-dimensional manifolds.

math-ph↗
arXiv2010

Bubble divergences from cellular cohomology

We consider a class of lattice topological field theories, among which are the weak-coupling limit of 2d Yang-Mills theory, the Ponzano-Regge model of 3d quantum gravity and discrete BF theory, whose dynamical variables are flat discrete connections with compact structure group on a cell 2-complex. In these models, it is known that the path integral measure is ill-defined in general, because of a phenomenon called `bubble divergences'. A common expectation is that the degree of these divergences is given by the number of `bubbles' of the 2-complex. In this note, we show that this expectation, although not realistic in general, is met in some special cases: when the 2-complex is simply connected, or when the structure group is Abelian -- in both cases, the divergence degree is given by the second Betti number of the 2-complex.

gr-qc↗
arXiv2009

Scaling behaviour of three-dimensional group field theory

Group field theory is a generalization of matrix models, with triangulated pseudomanifolds as Feynman diagrams and state sum invariants as Feynman amplitudes. In this paper, we consider Boulatov's three-dimensional model and its Freidel-Louapre positive regularization (hereafter the BFL model) with a ?ultraviolet' cutoff, and study rigorously their scaling behavior in the large cutoff limit. We prove an optimal bound on large order Feynman amplitudes, which shows that the BFL model is perturbatively more divergent than the former. We then upgrade this result to the constructive level, using, in a self-contained way, the modern tools of constructive field theory: we construct the Borel sum of the BFL perturbative series via a convergent ?cactus' expansion, and establish the ?ultraviolet' scaling of its Borel radius. Our method shows how the ?sum over trian- gulations' in quantum gravity can be tamed rigorously, and paves the way for the renormalization program in group field theory.

hep-th↗
arXiv2009

Towards the graviton from spinfoams: the complete perturbative expansion of the 3d toy model

We consider an exact expression for the 6j-symbol for the isosceles tetrahedron, involving integrals over SU(2), and use it to write the two-point function of 3d gravity on a single tetrahedron as a group integral. The perturbative expansion of this expression is then performed with respect to the boundary geometry using a simple saddle-point analysis. We derive the complete expansion in inverse powers of the length scale and evaluate explicitly the quantum corrections up to second order. Finally, we use the same method to provide the complete expansion of the isosceles 6j-symbol with the explicit phases at all orders and the next-to-leading correction to the Ponzano-Regge asymptotics.

gr-qc↗
arXiv2007

Relational EPR

We study the EPR-type correlations from the perspective of the relational interpretation of quantum mechanics. We argue that these correlations do not entail any form of 'non-locality', when viewed in the context of this interpretation. The abandonment of strict Einstein realism implied by the relational stance permits to reconcile quantum mechanics, completeness, (operationally defined) separability, and locality.

quant-ph↗