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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## Oh no, there’s been an error

Here, we develop the generalisation to SL 2,Cthat is we use twistors to parametrise the phase space of self-dual holonomy-flux variables. A very important aspect of the Hamiltonian operator is that it only acts at vertices a consequence of this is that Thiemann’s Hamiltonian operator, like Ashtekar’s operator, annihilates non-intersecting loops except now it is not just formal and has rigorous mathematical meaning.

However, the understanding of diffeomorphisms involving time the Hamiltonian constraint is more subtle because it is related to dynamics and the so-called ” problem of time ” in general relativity. Theories of gravitation Loop quantum gravity Physics beyond the Standard Model. For example, string theory also addresses unificationthe understanding of all known forces and particles as manifestations of a single entity, by postulating extra dimensions and so-far unobserved additional particles and symmetries.

With analogy to the Fourier integral given above, this generalized projector can formally be written as. Donc, euh, faudrait que je…. It turns out that a similar trick can be used to treat the second term. La correction des copies de Nozman en direct dans Podcast science Robin: LQG never introduces a background and excitations living on this background, so LQG does not use gravitons as building blocks.

This is equivalent to leaving everything else fixed while shifting the smearing. They may help reconcile the spin foam and canonical loop representation approaches. Let us consider constrained systems, of which General relativity is an example. Squaring the constraint is dangerous as it could lead to worsened ultraviolet behaviour of the corresponding operator and hence the master constraint programme must be approached with due care. The energy of those fluctuations at scales this small cause space-perturbations which are visible at higher scales.

La nuit, tous les arbres sont-ils gris? Thus we have identified an infinite set of exact if only formal solutions to all the equations of quantum general relativity! So we have something like.

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

Euh, oui, mais du coup, enfin, elles sont pas totalement inobservables. Space’s structure prefers an extremely fine fabric or network woven of finite loops. The feature that distinguishes such different theories is the Hamiltonian constraint which is the only one that depends on the Lagrangian of the classical theory. Many of the technical problems in canonical quantum gravity revolve around the constraints.

Bosonic string theory M-theory Supergravity Superstring theory. Of particular importance is the Poisson bracket algebra formed between the smeared constraints themselves as it completely determines the theory. Wolfgang Martin Wieland 1 AuthorId: What is preserved under such transformations are the coincidences between the values the gravitational field take at such and such a “place” and the values the matter fields take there. Progress has been made in calculating background independent scattering amplitudes this way with the use of spin foams.

Finally, the last aspect of this research studies the dynamics of the boundary interacting with an environment whose degrees of freedom gravitational or matter forming the rest of the Universe and especially bouclees decoherence it induces.

An advantage of the extended master constraint is that we are working at the kinematic level and so far it is only here we have access semiclassical coherent states. This is extremely important because, as noted above, the Poisson bracket algebra formed between the smeared constraints themselves quantiquf determines the classical theory. In terms of the above smeared constraints the constraint algebra amongst the Gauss’ law reads.

It is possible to derive, from the covariant formulation of full quantum theory Spinfoam the correct relation between energy and area 1st law quanfique, the Unruh temperature and the distribution that yields Hawking entropy.

Let us go into more detail about the technical difficulties associated with using Ashtekar’s variables:.

Parce que le trou noir… David: This then naturally gives rise to the two-complex a combinatorial set of faces that join along edges, which in turn join on vertices underlying the spin foam description; we evolve forward an initial spin network sweeping out a surface, the action of the Hamiltonian constraint operator is to produce a new planar surface starting at the vertex.

As Carlo Rovelli puts it: LQG and related research programs. Since gravitatioh action is a polynomial in the spinors, canonical quantisation is straightforward.

## Loop quantum gravity

The dynamics of such a theory are thus very different from that of ordinary Yang—Mills theory. Another difficulty here is that spin foams are defined on a discretization of spacetime.

Here we just mention issues that arises with the Hamiltonian constraint. The background dependence of string theory bouclse have important physical consequences, such as determining the number of quark generations. This framework was originally introduced by Freidel and Speziale, but only for the case of SU 2 Ashtekar–Barbero variables.

### Gravitation quantique a boucles by Podcast Science – Listen to music

However, there is no known computation of the Immirzi parameter, so it had to be fixed by demanding agreement with Bekenstein and Hawking’s calculation of the black hole entropy.

Contrary to this, LQG is based only on quantum theory and general relativity and its scope is limited to understanding the quantum aspects of the gravitational quantiqe.

Loop quantum gravity LQG is a theory of quantum gravitymerging quantum mechanics and general relativitymaking it a possible candidate for a theory of everything. Isolated horizon boundary degrees of freedom”.

That is, we construct what mathematicians call knot invariants. We will then discuss the spinfoam dynamics in terms of these twistorial variables, and arrive at our third result: See the article Self-dual Palatini action for a derivation of Ashtekar’s formulism.

Causal dynamical triangulation Causal sets Noncommutative geometry Bokcles foam Group field theory Superfluid vacuum theory Twistor theory Dual graviton.

String theory Loop quantum gravity Causal dynamical triangulation Canonical quantum gravity Superfluid vacuum theory Twistor theory. It comes in two versions.

We can see the analogy with going to the momentum representation in quantum mechanics see Position and momentum space.