This series consists of talks in the area of Quantum Gravity.
In this talk I will describe a topos formulation of consistent histories obtained using the topos reformulation of standard quantum mechanics put forward by Doering and Isham. Such a reformulation leads to a novel type of logic with which to represent propositions. In the first part of the talk I will introduce the topos reformulation of quantum mechanics. I will then explain how such a reformulation can be extended so as to include temporally-ordered collection of propositions as opposed to single time propositions.
The handling of the constraints on initial data is a major issue in most canonical formulations of general relativity. Since the 1960s unconstrained initial data for GR that living on null hypersurfaces has been known, but no canoncial formulation based on these data was developed due to conceptual and technical difficulties. I will explain how these dificulties have been overcome and outline the resulting canonical framework.
Using 2-dimensional CGHS black holes, I will argue that information is not lost in the Hawking evaporation because the quantum space-time is significantly larger than the classical one. I will begin with a discussion of the conceptual underpinnings of problem and then introduce a general, non-perturbative framework to describe quantum CGHS black holes. I will show that the Hawking effect emerges from it in the first approximation.
As well known, cosmic ray experiments can put strong constraints on possible Lorentz Invariance Violations. In particular, the presence of the so called GZK \'cut-off\' may indicate that protons do propagate in the Universe as expected from relativistic invariance. The presence of this feature in the spectrum has been convincingly indicated by the HiRes and Auger experiments, while the Auger Observatory has given indication on the correlation of Ultra High Energy Cosmic particles with nearby sources, as predicted by the GZK feature.
Motivated by the analogy proposed by Witten between Chern-Simons theories and CFT-Wess-Zumino-Witten models, we explore a new way of computing the entropy of a black hole starting from the isolated horizon framework in Loop Quantum Gravity. The results seem to indicate that this analogy can work in this particular case. This could be a good starting point for the search of a deeper connection between the description of black holes in LQG and a conformal field theory.
I discuss a class of compact objects (\'monsters\') with more entropy than a black hole of the same ADM mass. Such objects are problematic for AdS/CFT duality and the conventional interpretation of black hole entropy as counting of microstates. Nevertheless, monster initial data can be constructed in semi-classical general relativity without requiring large curvatures or energy densities.
The semiclassical-quantum correspondence (SQC) is a new principle which has enabled the explicit solution of the quantum constraints of GR in the full theory in the Ashtekar variables for gravity coupled to matter. The solutions, which constitute the physical space of states implementing the quantum dynamics of GR in the Dirac procedure, include a special class of states known as the generalized Kodama states (GKod). The GKodS can be seen as an analogue of the pure Kodama state (Kod) when quantum gravity (QGRA) is coupled to matter fields quantized on the same footing.
We discuss the possibility that spacetime geometry may be an emergent phenomenon. This idea has been motivated by the Analogue Gravity programme. An \'effective gravitational field\' dominates the kinematics of small perturbations in an Analogue Model. In these models there is no obvious connection between the \'gravitational\' field tensor and the Einstein equations, as the emergent spacetime geometry arises as a consequence of linearising around some classical field. After a brief introduction on this topic, we present our recent contributions to the field.
After reviewing Wilson\'s picture of renormalization, and the associated Exact Renormalization Group, I will show that no (physically acceptable) non-trivial fixed points exist for scalar field theory in D>=4. Consequently, an asymptotic safety scenario is ruled out, and the triviality of the theory is confirmed.
In an asymptotically anti-de Sitter space, three-dimensional topologically massive gravity has some remarkable properties, which suggest interesting applications to quantum gravity. Unfortunately, though, the theory appears to be unstable, even at the special \'chiral\' value of the coupling. I will discuss recent work, and recent controversies, in this field.