DEVELOPPEMENT MATHEMATIQUE ET APPLICATIONS DE LA GRAVITATION QUANTIQUE A BOUCLES. Thesis (PDF Available) · January. Des chercheurs de l’Institut Périmètre travaillent activement sur un certain nombre d’approches de ce problème, dont la gravitation quantique à boucles, les . 19 avr. A quantum theory of gravitation aims at describing the gravitational La gravité quantique à boucles étant toujours une théorie en cours de.

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It would therefore be desirable to have higher-dimensional Supergravity loop quantizations at one’s disposal in order to compare these approaches. The equations of LQG are not embedded in, or dependent on, space and time except for its invariant topology. This allows to discuss the quantum to classical transition and understand, in a given model, the pointer states of geometry. This was a huge simplification and eventually initiated the program of loop quantum gravity.

The constraints in their primitive form are rather singular, this was the reason for integrating them over test functions to obtain smeared constraints. It turns out that the master constraint is easily generalized to incorporate the other constraints.

Let us go back to the connection representation. Cette condition sur l’absence de torsion est en fait une contrainte secondaire de l’analyse canonique. This is formally spatially diffeomorphism-invariant. Black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons.

It may turn out that LQG belongs to an unphysical sector — one in which one does not recover general relativity in the semiclassical limit in fact there might not be any physical sector at all. Instead one expects that one may recover a kind of semiclassical limit or weak field limit where something like “gravitons” will show up again.

These networks of loops are called spin networks. Paradigms Classical theories of gravitation Quantum gravity Theory of everything. Et donc il y a eu beaucoup de modifications depuis 30, euh 40 ans maintenant.

As Carlo Rovelli puts it: The master constraint see below does not suffer from these problems and as such offers a way of connecting the canonical theory to the path integral formulation. Quantum gravity effects are notoriously difficult to measure because the Planck length is so incredibly small. This is the connection representation.


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Some quantum theories of gravity posit a spin-2 quantum field that is quantized, giving rise to gravitons. InRovelli and Smolin showed that the quantum operators of the theory associated to area and volume have a discrete spectrum. In theoretical physics, general covariance is the invariance of the form of physical laws under arbitrary differentiable coordinate transformations.

This defines the loop representation. Chapter four studies the resulting quantum theory. These reality conditions match the linear simplicity constraints of spinfoam gravity. Because of its significance this is known as the master equation. The Immirzi parameter also known as the Barbero-Immirzi parameter is a numerical coefficient appearing in loop quantum gravity.

As Wilson loops form a basis we can formally expand any Gauss gauge invariant function as. Spinfoam gravity, on the other hand, takes a covariant path integral representation to define the transition amplitudes of the theory.

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The theory gives a physical picture of spacetime where space and time are granular and discrete directly because of quantization just like photons in the quantum theory of electromagnetism and the discrete energy levels of atoms. The sum over rerouting are chosen as such to make the form of the intertwiner invariant under Gauss gauge transformations. There is the consistent discretizations approach. The canonical version of the dynamics was put on firm ground by Thomas Thiemannwho defined an anomaly-free Hamiltonian operator, showing the existence of a mathematically consistent background-independent theory.

The corresponding phase space has a non-linear structure.

Parce que le trou noir…. The gauge motions of the constraints apply to all phase space but have the feature that they leave the constraint surface where it is, and thus bouclse orbit of a point in the hypersurface under gauge transformations will be an orbit entirely within it.

Entanglement and Decoherence in Loop Quantum Gravity. The popular and technical literature makes extensive references to LQG-related topic of loop quantum cosmology.

Donc on peut avoir un univers quasiment ponctuel mais infini. Diffeomorphismsas mathematicians define them, correspond to something much more radical; intuitively a way they can be envisaged is as simultaneously dragging all the physical fields including the gravitational field over the bare differentiable manifold while staying in the same coordinate system.


The problem was that although Loop quantum gravity predicted that the entropy of a black hole is gravittaion to the area of the event horizon, the result depended on a crucial free parameter in the theory, the above-mentioned Immirzi parameter. Before we move on to the constraints of LQG, lets us consider certain cases. This is the second result.

This is a simpler theory than general relativity, it has no local degrees of freedom and as such depends only quantiquue topological aspects of the fields. So one always has. This quantity is important in the final formula for the area spectrum. This represents a dramatic simplification of the Poisson bracket structure, and raises new hope in understanding the dynamics and establishing buocles semiclassical limit.

A strategy for addressing this problem has been suggested; [66] the idea is to study the boundary amplitude, namely a path integral over a finite space-time region, seen as a function of the boundary value of the quanntique. Since loop quantum gravity is still under construction, a pragmatic point of view is advocated and an ansazt for physical states of the gravitational field is studied at first, motivated from condensed matter physics and simple intuitions.

The canonical approach seeks to solve the Wheeler–DeWitt equation auantique find the physical states of the theory. That the master constraint Poisson algebra is an honest Lie algebra opens up the possibility of using a certain method, known as group averaging, in order to construct solutions of the infinite number of Hamiltonian constraints, a physical inner product thereon and Dirac quamtique via what is known as refined algebraic quantization RAQ. The use of Wilson loops explicitly solves the Gauss gauge constraint.


Before this result was established it was not known whether there could be other examples of Hilbert spaces with operators invoking the same loop algebra, other realizations, not equivalent to the one that had been used so far.