By Vincent Rivasseau (Chief Editor)
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Extra info for Annales Henri Poincaré - Volume 4 - Supplements
Thus, in contrast to approaches developed by particle physicists, one does not begin with quantum matter on a background geometry and use perturbation theory to incorporate quantum eﬀects of gravity. 1 In classical gravity, Riemannian geometry provides the appropriate mathematical language to formulate the physical, kinematical notions as well as the ﬁnal dynamical equations. This role is now taken by quantum Riemannian geometry, discussed below. In the classical domain, general relativity stands out as the best available theory of gravity, some of whose predictions have been tested to an amazing accuracy, surpassing even the legendary tests of quantum electrodynamics.
More precisely, what is the statistical mechanical origin of black hole entropy? What is the nature of a quantum black hole and what is the interplay between the quantum degrees of freedom responsible for entropy and the exterior curved geometry? Can one derive the Hawking eﬀect from ﬁrst principles of quantum gravity? Recent advances in quantum geometry have provided illuminating answers to several of these questions and opened-up avenues to address others. There are also S56 Abhay Ashtekar Ann.
For mD the dominance of the third family eigenvalue as well as a near diagonal form could be an order of magnitude remnant of this broken symmetry. Thus, neglecting small terms, the neutrino Dirac matrix in the basis where charged leptons are diagonal could be directly obtained in the form of eq. (15). 4 Conclusion While the existence of oscillations appears to be on a ground of increasing solidity, many important experimental challenges remain. For atmospheric neutrino oscillations the completion of the K2K experiment, now stopped by the accident that has seriously damaged the Superkamiokande detector, is important for a terrestrial conﬁrmation of the eﬀect and for an independent measurement of the associated S52 Guido Altarelli Ann.
Annales Henri Poincaré - Volume 4 - Supplements by Vincent Rivasseau (Chief Editor)