Mexi Lazos 2012

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Tenemos el agrado de invitarlos a Mexi-Lazos 2012 a celebrarse el viernes 9 y sábado 10 de noviembre en las instalaciones del Centro de Ciencias Matemáticas, UNAM, Morelia.

Se tratará de dar un panorama general sobre los avances y retos en el entendimiento de los grados de libertad de los agujeros negros, desde la perspectiva de LQG. Se mencionará el acercamiento ya clásico al problema, así como avances recientes y se discutirá en detalle las limitaciones y retos que aun existen.

I review the structure of canonical loop quantized theories, and how covariant loop quantized theories provide a path integral that defines relative amplitudes for given boundary data. The mentioned amplitudes that determine the dynamics are only defined if certain limits exist. The presented formalism unifies the canonical and covariant approaches to loop quantization. Then, I critically review the issue of actually constructing nontrivial loop quantized theories.

The standard formulation of quantum theory in terms of a Hilbert space with operators relies on an absolute notion of background time at its very core. On the other hand, the dynamical nature of spacetime is at the very basis of general relativity. This violent tension throws into serious doubt any enterprise that aims at finding a quantum theory of gravity based on the standard formulation of quantum theory. In contrast, the general boundary formulation (GBF) of quantum theory is fully compatible with a dynamic nature of spacetime and thus a much more natural home for a quantum theory of gravity. I give a basic introduction to the GBF and proceed to show how spin foam models form part of an approach to quantum gravity within the GBF.

We review the general program of effective canonical equations in Loop Quantum Gravity. By imposing consistency conditions, particularly anomaly freedom, one may derive candidate effective equations to extract information about dynamics and the structure of quantum space-time. We draw examples mainly from the spherically symmetric sector of the theory.