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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Loop quantum gravity – Wikipedia

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. It is possible to extend mainstream LQG formalism to higher-dimensional supergravity, general relativity with supersymmetry and Kaluza—Klein extra dimensions should experimental evidence establish their existence. It comes in two versions. Modern Canonical General Relativity.

Thus, one is forced to work with the original unrescaled, density one-valued, Hamiltonian constraint. The spatial diffeomorphism constraint with a Hamiltonian gives a Hamiltonian with its smearing shifted. Il y a des grandes choses que vous le connaissiez. So the master constraint does capture information about the observables. We consider the action of the constraints on arbitrary phase space functions. Another difficulty here is that spin foams are defined on a discretization of spacetime.

Isolated horizon boundary degrees garvitation freedom”.

The Chiral Structure of Loop Quantum Gravity

In contrast, gravitons play a key role in string theory where they are among the boucpes massless level of excitations of a superstring. Shortly after, Gravitatiion Jacobson and Lee Smolin realized that the formal equation of quantum gravity, called the Wheeler—DeWitt equationadmitted solutions labelled by loops when rewritten in the new Ashtekar variables. Canonical general relativity was originally formulated in terms of metric quantiquee, but there seemed to be insurmountable mathematical difficulties in promoting the constraints to quantum operators because of their highly non-linear dependence on the canonical variables.


This defines the loop representation. Loop quantum gravity, like string theory, also aims to overcome the nonrenormalizable divergences of quantum field theories. The Consistent Discretizations approach to LQG, [46] [47] is an application of the master constraint program to construct the physical Hilbert space of the canonical theory. That is, geometry is quantized.


Ordinary measurements of geometric quantities are macroscopic, and planckian discreteness is smoothed out. According to Einstein, gravity is not a force — it is a property of spacetime itself. Les plantes dorment la nuit: Let us go into more detail about the technical difficulties associated with using Ashtekar’s variables:.

As far as gtavitation currently known, problem 4 of having semiclassical machinery for non-graph changing operators is at the moment still out of reach. Est ce que tu as un avis, David? The classical limit or correspondence limit is the ability of a physical theory to approximate or “recover” classical mechanics when considered over special values of its parameters. Enfin, si, un tout petit peu avant. However, the understanding of diffeomorphisms involving time the Hamiltonian grqvitation is more subtle because it is related to dynamics and the so-called ” problem of time ” in general relativity.

Carlo Rovelli and Lee Smolin defined quantque nonperturbative and background-independent quantiaue theory of gravity in terms of these loop solutions. 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.


There were serious difficulties in promoting this quantity to a quantum operator. This is an unavoidable consequence of the operator algebra, in particular the commutator:. For a number of technical reasons the complex variables have later been abandoned in favour of the SU 2 Ashtekar–Barbero variables, and the simplification of the Hamiltonian constraint was lost again.

Specifically, in LQG [53] it is possible to associate a quantum geometrical interpretation to the microstates: A quantum theory of gravitation aims at describing the gravitational interaction at every scales of energy and distance. BF theory is what is known as a topological field theory. Moreover, one boudles find none graph changing versions of this master constraint operator, which are the only type of operators appropriate for these coherent states.

Simulated Large Hadron Collider CMS particle detector data depicting a Higgs boson produced by colliding protons decaying into hadron jets and electrons. However, it was realized that the condition. Les physiciens nous donnent raison.

Inclusion of distortion and rotation”. Instead one expects that one may recover a kind of semiclassical limit or weak field limit where something like “gravitons” will show up again.