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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Of particular importance is the Poisson bracket algebra formed between the smeared constraints themselves as it completely determines the theory. This is formally spatially diffeomorphism-invariant. Let us consider constrained systems, of which General relativity is an example.

In LQG this aspect of general relativity is taken seriously and this symmetry is preserved by requiring that the physical states remain invariant under the generators of diffeomorphisms. We now consider Wilson loops with intersections. Podcast Science — Etes vous assez paresseux pour devenir riches…. The easiest geometric quantity is the area.

Loop quantum gravity is formulated in a background-independent language. The first attempt at this was the famous Barrett—Crane model. The constraints define a constraint surface in the original phase space.

## Loop quantum gravity

In mathematics, a diffeomorphism is an isomorphism in the category of smooth manifolds. These smeared constraints defined with respect to a suitable space of smearing functions give an equivalent description to the original constraints.

Alors, on sait pas en fait. Holonomies can also be associated with an edge; under a Gauss Law these transform as.

It competes with string theory that begins with quantum field theory and adds gravity. When one quantizes the theory, it is difficult to ensure that one recovers real general relativity as opposed to complex general relativity. In real Gragitation variables the Hamiltonian is.

### TEL – Thèses en ligne – Entanglement and Decoherence in Loop Quantum Gravity

Without the implementation and solution of the Hamiltonian constraint no progress can be made and no reliable predictions are possible. However recently physicists have started to consider the possibility of measuring quantum gravity effects mostly from astrophysical observations and gravitational bboucles detectors.

Quantum gravity effects are notoriously difficult to measure because the Planck length is so incredibly small. In particular, one can calculate the scattering amplitudes from these quantities. Now just as a spin networks describe quantum ggravitation, each configuration contributing to these path integrals, or sums over history, describe ‘quantum space-time’. This dramatic simplification seemed to open up the way to quantizing the constraints.

To recover the real theory, one has to impose grqvitation are known as the “reality conditions. In contrast, loop quantum gravity, like general relativity, is manifestly background independent, eliminating the background required in string theory. So we have something like. The master constraint programme has evolved into a fully combinatorial treatment of gravity known as Algebraic Quantum Gravity AQG.

According to Einstein, gravity is not a force — it is a property of quantiqke itself. Just as different phases are physically different, so are different sectors of a quantum field theory.

It turns gravitatoin there are alternative routes to formulating the path integral, however their connection to the Hamiltonian formalism is less clear.

New Theory on the Universe’s Birth”. These are the defining symmetry transformations of General Relativity since the theory is formulated only in terms of a differentiable manifold.

### TEL – Thèses en ligne – The Chiral Structure of Loop Quantum Gravity

Knowledge of the holonomies is equivalent to knowledge of the connection, up to gauge equivalence. Paradigms Classical theories of gravitation Quantum gravity Buocles of everything. This result defines an explicit basis of states of quantum geometry, which turned out to be labelled by Roger Penrose ‘s spin networkswhich are graphs labelled by spins.

The quqntique of background independence in LQG still has some unresolved subtleties. This defines the loop representation. Quantum gravity Quantum information Entanglement Decoherence.

## Retranscription: la gravité quantique à boucles

Cette condition sur l’absence de torsion est en fait une contrainte secondaire de l’analyse canonique. The problem was that although Loop quantum gravity predicted that the entropy of a black hole is proportional to the area of the event horizon, the result depended on a crucial free parameter in the theory, the above-mentioned Immirzi parameter.

The essential idea is that coordinates are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws. Probed at a macroscopic scale, it appears as a three-dimensional continuous metric geometry. In doing so the master constraint programme has been satisfactorily tested in a number of model systems with non-trivial constraint algebras, free and interacting field theories.

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