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Carlo Rovelli

Publications and source records attributed to Carlo Rovelli.

At least 181 records · Page 10Linked to original sources
arXiv2007

The loop-quantum-gravity vertex-amplitude

Spinfoam theories are hoped to provide the dynamics of non-perturbative loop quantum gravity. But a number of their features remain elusive. The best studied one -the euclidean Barrett-Crane model- does not have the boundary state space needed for this, and there are recent indications that, consequently, it may fail to yield the correct low-energy $n$-point functions. These difficulties can be traced to the SO(4) -> SU(2) gauge fixing and the way certain second class constraints are imposed, arguably incorrectly, strongly. We present an alternative model, that can be derived as a bona fide quantization of a Regge discretization of euclidean general relativity, and where the constraints are imposed weakly. Its state space is a natural subspace of the SO(4) spin-network space and matches the SO(3) hamiltonian spin network space. The model provides a long sought SO(4)-covariant vertex amplitude for loop quantum gravity.

gr-qc↗
arXiv2007

Compatibility of radial, Lorenz and harmonic gauges

We observe that the radial gauge can be consistently imposed \emph{together} with the Lorenz gauge in Maxwell theory, and with the harmonic traceless gauge in linearized general relativity. This simple observation has relevance for some recent developments in quantum gravity where the radial gauge is implicitly utilized.

gr-qc↗
arXiv2007

Multiple-event probability in general-relativistic quantum mechanics: a discrete model

We introduce a simple quantum mechanical model in which time and space are discrete and periodic. These features avoid the complications related to continuous-spectrum operators and infinite-norm states. The model provides a tool for discussing the probabilistic interpretation of generally-covariant quantum systems, without the confusion generated by spurious infinities. We use the model to illustrate the formalism of general-relativistic quantum mechanics, and to test the definition of multiple-event probability introduced in a companion paper. We consider a version of the model with unitary time-evolution and a version without unitary time-evolution

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↗
arXiv2006

Multiple-event probability in general-relativistic quantum mechanics

We discuss the definition of quantum probability in the context of "timeless" general--relativistic quantum mechanics. In particular, we study the probability of sequences of events, or multi-event probability. In conventional quantum mechanics this can be obtained by means of the ``wave function collapse" algorithm. We first point out certain difficulties of some natural definitions of multi-event probability, including the conditional probability widely considered in the literature. We then observe that multi-event probability can be reduced to single-event probability, by taking into account the quantum nature of the measuring apparatus. In fact, by exploiting the von-Neumann freedom of moving the quantum classical boundary, one can always trade a sequence of non-commuting quantum measurements at different times, with an ensemble of simultaneous commuting measurements on the joint system+apparatus system. This observation permits a formulation of quantum theory based only on single-event probability, where the results of the "wave function collapse" algorithm can nevertheless be recovered. The discussion bears also on the nature of the quantum collapse.

gr-qc↗
arXiv2006

A semiclassical tetrahedron

We construct a macroscopic semiclassical state state for a quantum tetrahedron. The expectation values of the geometrical operators representing the volume, areas and dihedral angles are peaked around assigned classical values, with vanishing relative uncertainties.

gr-qc↗
arXiv2006

Unfinished revolution

Introductive chapter of a book on Quantum Gravity, edited by Daniele Oriti, to appear with Cambridge University Press.

gr-qc↗
arXiv2006

From 3-geometry transition amplitudes to graviton states

In various background independent approaches, quantum gravity is defined in terms of a field propagation kernel: a sum over paths interpreted as a transition amplitude between 3-geometries, expected to project quantum states of the geometry on the solutions of the Wheeler-DeWitt equation. We study the relation between this formalism and conventional quantum field theory methods. We consider the propagation kernel of 4d Lorentzian general relativity in the temporal gauge, defined by a conventional formal Feynman path integral, gauge fixed a\' la Fadeev--Popov. If space is compact, this turns out to depend only on the initial and final 3--geometries, while in the asymptotically flat case it depends also on the asymptotic proper time. We compute the explicit form of this kernel at first order around flat space, and show that it projects on the solutions of all quantum constraints, including the Wheeler-DeWitt equation, and yields the correct vacuum and n-graviton states. We also illustrate how the Newtonian interaction is coded into the propagation kernel, a key open issue in the spinfoam approach.

gr-qc↗
arXiv2005

Graviton propagator from background-independent quantum gravity

We study the graviton propagator in euclidean loop quantum gravity, using the spinfoam formalism. We use boundary-amplitude and group-field-theory techniques, and compute one component of the propagator to first order, under a number of approximations, obtaining the correct spacetime dependence. In the large distance limit, the only term of the vertex amplitude that contributes is the exponential of the Regge action: the other terms, that have raised doubts on the physical viability of the model, are suppressed by the phase of the vacuum state, which is determined by the extrinsic geometry of the boundary.

gr-qc↗
arXiv2005

On the perturbative expansion of a quantum field theory around a topological sector

The idea of treating general relativistic theories in a perturbative expansion around a topological theory has been recently put forward in the quantum gravity literature. Here we investigate the viability of this idea, by applying it to conventional Yang--Mills theory on flat spacetime. We find that the expansion around the topological theory coincides with the usual expansion around the abelian theory, though the equivalence is non-trivial. In this context, the technique appears therefore to be viable, but not to bring particularly new insights. Some implications for gravity are discussed.

gr-qc↗
arXiv2005

Physical effects of the Immirzi parameter

The Immirzi parameter is a constant appearing in the general relativity action used as a starting point for the loop quantization of gravity. The parameter is commonly believed not to show up in the equations of motion, because it appears in front of a term in the action that vanishes on shell. We show that in the presence of fermions, instead, the Immirzi term in the action does not vanish on shell, and the Immirzi parameter does appear in the equations of motion. It determines the coupling constant of a four-fermion interaction. Therefore the Immirzi parameter leads to effects that are observable in principle, even independently from nonperturbative quantum gravity.

gr-qc↗
arXiv2005

Particle scattering in loop quantum gravity

We devise a technique for defining and computing n-point functions in the context of a background-independent gravitational quantum field theory. We construct a tentative implementation of this technique in a perturbatively-finite loop/spinfoam model.

gr-qc↗
arXiv2005

Black hole entropy: inside or out?

A trialogue. Ted, Don, and Carlo consider the nature of black hole entropy. Ted and Carlo support the idea that this entropy measures in some sense ``the number of black hole microstates that can communicate with the outside world.'' Don is critical of this approach, and discussion ensues, focusing on the question of whether the first law of black hole thermodynamics can be understood from a statistical mechanics point of view.

hep-th↗
arXiv2004

Spinfoam 2d quantum gravity and discrete bundles

In 4 dimensions, general relativity can be formulated as a constrained $BF$ theory; we show that the same is true in 2 dimensions. We describe a spinfoam quantization of this constrained BF-formulation of 2d riemannian general relativity, obtained using the Barrett-Crane technique of imposing the constraint as a restriction on the representations summed over. We obtain the expected partition function, thus providing support for the viability of the technique. The result requires the nontrivial topology of the bundle where the gravitational connection is defined, to be taken into account. For this purpose, we study the definition of a principal bundle over a simplicial base space. The model sheds light also on several other features of spinfoam quantum gravity: the reality of the partition function; the geometrical interpretation of the Newton constant, and the issue of possible finiteness of the partition function of quantum general relativity.

gr-qc↗
arXiv2004

Background independence in a nutshell

We study how physical information can be extracted from a background independent quantum system. We use an extremely simple `minimalist' system that models a finite region of 3d euclidean quantum spacetime with a single equilateral tetrahedron. We show that the physical information can be expressed as a boundary amplitude. We illustrate how the notions of "evolution" in a boundary proper-time and "vacuum" can be extracted from the background independent dynamics.

gr-qc↗
arXiv2004

Separable Hilbert space in Loop Quantum Gravity

We study the separability of the state space of loop quantum gravity. In the standard construction, the kinematical Hilbert space of the diffeomorphism-invariant states is nonseparable. This is a consequence of the fact that the knot-space of the equivalence classes of graphs under diffeomorphisms is noncountable. However, the continuous moduli labeling these classes do not appear to affect the physics of the theory. We investigate the possibility that these moduli could be only the consequence of a poor choice in the fine-tuning of the mathematical setting. We show that by simply choosing a minor extension of the functional class of the classical fields and coordinates, the moduli disappear, the knot classes become countable, and the kinematical Hilbert space of loop quantum gravity becomes separable.

gr-qc↗
arXiv2003

Generalized Schroedinger equation in Euclidean field theory

We investigate the idea of a "general boundary" formulation of quantum field theory in the context of the Euclidean free scalar field. We propose a precise definition for an evolution kernel that propagates the field through arbitrary spacetime regions. We show that this kernel satisfies an evolution equation which governs its dependence on deformations of the boundary surface and generalizes the ordinary (Euclidean) Schroedinger equation. We also derive the classical counterpart of this equation, which is a Hamilton-Jacobi equation for general boundary surfaces.

hep-th↗