Searcharxiv⌕ Search

arXiv subjects

Carlo Rovelli

Publications and source records attributed to Carlo Rovelli.

At least 145 records · Page 8Linked to original sources
arXiv2011

Discretizing parametrized systems: the magic of Ditt-invariance

Peculiar phenomena appear in the discretization of a system invariant under reparametrization. The structure of the continuum limit is markedly different from the usual one, as in lattice QCD. First, the continuum limit does not require tuning a parameter in the action to a critical value. Rather, there is a regime where the system approaches a sort of asymptotic topological invariance ("Ditt-invariance"). Second, in this regime the expansion in the number of discretization points provides a good approximation to the transition amplitudes. These phenomena are relevant for understanding the continuum limit of quantum gravity. I illustrate them here in the context of a simple system.

hep-lat↗
arXiv2011

A critical look at strings

This is an invited contribution to the Special Issue of "Foundations of Physics" titled "Forty Years Of String Theory: Reflecting On the Foundations". I have been asked to assess string theory as an outsider, and to compare it with the theory, methods, and expectations in my own field.

hep-th↗
arXiv2011

Simple model for quantum general relativity from loop quantum gravity

New progress in loop gravity has lead to a simple model of `general-covariant quantum field theory'. I sum up the definition of the model in self-contained form, in terms accessible to those outside the subfield. I emphasize its formulation as a generalized topological quantum field theory with an infinite number of degrees of freedom, and its relation to lattice theory. I list the indications supporting the conjecture that the model is related to general relativity and UV finite.

hep-th↗
arXiv2011

A note on the geometrical interpretation of quantum groups and non-commutative spaces in gravity

Quantum groups and non-commutative spaces have been repeatedly utilized in approaches to quantum gravity. They provide a mathematically elegant cut-off, often interpreted as related to the Planck-scale quantum uncertainty in position. We consider here a different geometrical interpretation of this cut-off, where the relevant non-commutative space is the space of directions around any spacetime point. The limitations in angular resolution expresses the finiteness of the angular size of a Planck-scale minimal surface at a maximum distance 1/\sqrt{Lambda} related the cosmological constant Lambda. This yields a simple geometrical interpretation for the relation between the quantum deformation parameter q=exp[i Lambda l_{Planck}^2 ] and the cosmological constant, and resolves a difficulty of more conventional interpretations of the physical geometry described by quantum groups or fuzzy spaces.

gr-qc↗
arXiv2011

Euclidean three-point function in loop and perturbative gravity

We compute the leading order of the three-point function in loop quantum gravity, using the vertex expansion of the Euclidean version of the new spin foam dynamics, in the region of gamma<1. We find results consistent with Regge calculus in the limit gamma->0 and j->infinity. We also compute the tree-level three-point function of perturbative quantum general relativity in position space, and discuss the possibility of directly comparing the two results.

gr-qc↗
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

Lorentz covariance of loop quantum gravity

The kinematics of loop gravity can be given a manifestly Lorentz-covariant formulation: the conventional SU(2)-spin-network Hilbert space can be mapped to a space K of SL(2,C) functions, where Lorentz covariance is manifest. K can be described in terms of a certain subset of the "projected" spin networks studied by Livine, Alexandrov and Dupuis. It is formed by SL(2,C) functions completely determined by their restriction on SU(2). These are square-integrable in the SU(2) scalar product, but not in the SL(2,C) one. Thus, SU(2)-spin-network states can be represented by Lorentz-covariant SL(2,C) functions, as two-component photons can be described in the Lorentz-covariant Gupta-Bleuler formalism. As shown by Wolfgang Wieland in a related paper, this manifestly Lorentz-covariant formulation can also be directly obtained from canonical quantization. We show that the spinfoam dynamics of loop quantum gravity is locally SL(2,C)-invariant in the bulk, and yields states that are preciseley in K on the boundary. This clarifies how the SL(2,C) spinfoam formalism yields an SU(2) theory on the boundary. These structures define a tidy Lorentz-covariant formalism for loop gravity.

gr-qc↗
arXiv2011

Cosmological constant in spinfoam cosmology

We consider a simple modification of the amplitude defining the dynamics of loop quantum gravity, corresponding to the introduction of the cosmological constant, and possibly related to the SL(2,C)q extension of the theory recently considered by Fairbairn-Meusburger and Han. We show that in the context of spinfoam cosmology, this modification yields the de Sitter cosmological solution.

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 new look at loop quantum gravity

I describe a possible perspective on the current state of loop quantum gravity, at the light of the developments of the last years. I point out that a theory is now available, having a well-defined background-independent kinematics and a dynamics allowing transition amplitudes to be computed explicitly in different regimes. I underline the fact that the dynamics can be given in terms of a simple vertex function, largely determined by locality, diffeomorphism invariance and local Lorentz invariance. I emphasize the importance of approximations. I list open problems.

gr-qc↗
arXiv2010

Local spinfoam expansion in loop quantum cosmology

The quantum dynamics of the flat Friedmann-Lemaitre-Robertson-Walker and Bianchi I models defined by loop quantum cosmology have recently been translated into a spinfoam-like formalism. The construction is facilitated by the presence of a massless scalar field which is used as an internal clock. The implicit integration over the matter variable leads to a nonlocal spinfoam amplitude. In this paper we consider a vacuum Bianchi I universe and show that by choosing an appropriate regulator a spinfoam expansion can be obtained without selecting a clock variable and that the resulting spinfoam amplitude is local.

gr-qc↗
arXiv2010

Generalized Spinfoams

We reconsider the spinfoam dynamics that has been recently introduced, in the generalized Kaminski-Kisielowski-Lewandowski (KKL) version where the foam is not dual to a triangulation. We study the Euclidean as well as the Lorentzian case. We show that this theory can still be obtained as a constrained BF theory satisfying the simplicity constraint, now discretized on a general oriented 2-cell complex. This constraint implies that boundary states admit a (quantum) geometrical interpretation in terms of polyhedra, generalizing the tetrahedral geometry of the simplicial case. We also point out that the general solution to this constraint (imposed weakly) depends on a quantum number r_f in addition to those of loop quantum gravity. We compute the vertex amplitude and recover the KKL amplitude in the Euclidean theory when r_f=0. We comment on the eventual physical relevance of r_f, and the formal way to eliminate it.

gr-qc↗
arXiv2010

On the geometry of loop quantum gravity on a graph

We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the "twisted geometries" and derive a simple relation between these and Regge geometries.

gr-qc↗
arXiv2010

Physical boundary Hilbert space and volume operator in the Lorentzian new spin-foam theory

A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we reconsider the implementation of the constraints that defines the model. We define in a simple way the boundary Hilbert space of the theory, introducing a slight modification of the embedding of the SU(2) representations into the SL(2,C) ones. We then show directly that all constraints vanish on this space in a weak sense. The vanishing is exact (and not just in the large quantum number limit.) We also generalize the definition of the volume operator in the spinfoam model to the Lorentzian signature, and show that it matches the one of loop quantum gravity, as does in the Euclidean case.

gr-qc↗
arXiv2010

Face amplitude of spinfoam quantum gravity

The structure of the boundary Hilbert-space and the condition that amplitudes behave appropriately under compositions determine the face amplitude of a spinfoam theory. In quantum gravity the face amplitude turns out to be simpler than originally thought.

gr-qc↗
arXiv2010

The volume operator in covariant quantum gravity

A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In particular, the geometrical observable giving the area of a surface has been shown to be the same as the one in loop quantum gravity. Here we discuss the volume observable. We derive the volume operator in the covariant theory, and show that it matches the one of loop quantum gravity, as does the area. We also reconsider the implementation of the constraints that defines the model: we derive in a simple way the boundary Hilbert space of the theory from a suitable form of the classical constraints, and show directly that all constraints vanish weakly on this space.

gr-qc↗
arXiv2010

Why all these prejudices against a constant?

The expansion of the observed universe appears to be accelerating. A simple explanation of this phenomenon is provided by the non-vanishing of the cosmological constant in the Einstein equations. Arguments are commonly presented to the effect that this simple explanation is not viable or not sufficient, and therefore we are facing the "great mystery" of the "nature of a dark energy". We argue that these arguments are unconvincing, or ill-founded.

astro-ph.CO↗