This series consists of talks in the area of Quantum Gravity.
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.
A modified version of the double potential formalism for the electrodynamics of dyons is constructed. Besides the two vector potentials, this manifestly duality invariant formulation involves four additional potentials, scalar potentials which appear as Lagrange multipliers for the electric and magnetic Gauss constraints and potentials for the longitudinal electric and magnetic fields. In this framework, a static dyon appears as a Coulomb-like solution without string singularities. Dirac strings are needed only for the Lorentz force law, not for Maxwell\'s equations.
The general boundary state formulation is a key tool for extracting the semiclassical limit of nonpertubative theories of quantum gravity. In this talk I will discuss how this formalism works in the context of four-dimensional quantum Regge calculus with a general triangulation. A Gaussian boundary state selects a classical internal solution and peaks the path integral on it. As a result boundary observables, in particular the two-point function, can be computed order by order in a semiclassical asymptotic expansion.
The standard Hamiltonian formulation of (first order) gravity breaks manifest covariance both in its retention of the Lorentz group as a local gauge group and in its discrepant treatment of spacelike and timelike diffeomorphisms. Here we promote more covariant alternatives for canonical quantum gravity that address each of these problems, and discuss the implications for both the classical and the quantum theory of gravity. By retaining the full local Lorentz group, one gains significant insight into the geometric and algebraic properties of the Hamiltonian dynamics.
During the last two decades Alain Connes developed Noncommutative Geometry, which allows to unify two of the basic theories of modern physics: General Relativity and the Standard Model of Particle Physics. In the noncommutative framework the Higgs boson, which had previously to be put in by hand, and many of the ad hoc features of the standard model, appear in a natural way. The aim of my talk is to motivate this unification from basic physical principles and to give a flavour of its derivation.
The speculation that Dark Energy can be explained by the backreaction of present inhomogeneities on the evolution of the background cosmology has been increasingly debated in the recent literature. We demonstrate quantitively that the backreaction of linear perturbations on the Friedmann equations is small but is nevertheless non-vanishing. This indicates the need for an improved averaging procedure capable of averaging tensor quantities in a generally covariant way.