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

Loop quantum gravity is formulated in a background-independent language. However, it would appear that the equation for the master constraint, given above, is gracitation more singular involving the product of two primitive constraints although integrated over space. Version validated by the jury STAR.

The physical inner product is then defined as. To make contact with familiar low energy physics it is mandatory voucles have to develop approximation schemes both for the physical inner product and for Dirac observables.

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Loop quantum cosmologyBig wuantiqueand inflation cosmology. Presently, no semiclassical limit recovering general relativity has been shown to exist. This is called the loop transform. We also have the usual algebra between spatial diffeomorphisms. The dynamics of general relativity is generated by the constraints, it can be shown that six Einstein equations describing time evolution really a gauge transformation can be obtained by calculating the Poisson brackets of the three-metric and its conjugate momentum with a linear combination of the spatial diffeomorphism and Hamiltonian constraint.


Typiquement, est ce que le boson existe? The theory gives a physical picture of spacetime where space and time are granular and discrete directly because of quantization just quantiqye photons in the quantum theory of electromagnetism and the discrete energy levels of atoms.

We can see the analogy with going to the momentum representation in quantum mechanics see Position and momentum space. Lessons on the quantum dynamics and the Hamiltonian constraint are extracted.

Enfin, cette … David: Diffeomorphisms are the true symmetry transformations of general relativity, and come about from the assertion that the formulation of the theory is based on a bare differentiable manifold, but not on any prior geometry — the theory is background-independent this is a profound shift, as all physical theories before general relativity had as part of their formulation a prior geometry.

The most fundamental representation being the Pauli matrices. 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.

One does not actually need to promote the Gauss constraint to an operator since we can work directly with Gauss-gauge-invariant functions that is, one solves the constraint classically and quantizes only the phase space reduced with respect to the Gauss constraint. Salut tous le monde Johan: The expressions for the constraints in Ashtekar variables; the Gauss’s law, the spatial diffeomorphism constraint and the densitized Hamiltonian constraint then read:.

This quantity is important in the final formula for the area spectrum.


The Chiral Structure of Loop Quantum Gravity

But problems similar to using the metric formulation arise when one tries to quantize the theory. This is formally spatially diffeomorphism-invariant.

These identities can be combined with each other into further identities of increasing complexity adding more loops. The non-trivial task of constructing a spin foam model is then reduced to the question of how this simplicity constraint should be imposed in the quantum theory.

Spin networks certain are linear combinations of intersecting Wilson loops designed to address the over completeness introduced by the Mandelstam identities for trivalent intersections they eliminate the over-compleness entirely and actually constitute a basis for all gauge invariant functions. There are substantial differences however.

Some quantum theories of gravity posit a spin-2 quantum field that is quantized, giving rise to gravitons. Modern Canonical General Relativity. So we have something like. This is known as the problem triangularization dependence. This is an unavoidable consequence of the operator algebra, grvaitation particular the commutator:.

The action is a sum of the spinorial analogue of the topological BF-action and the reality conditions that guarantee the existence of a metric. The kinematic inner product structure is easily employed to provide the inner product structure after solving this first constraint; the new inner product is simply.

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