Quantizing Geometry or Geometrizing the Quantum?

The unsatisfactory status of the search for a consistent and predictive quantization of gravity is taken as motivation to study the question whether geometrical laws could be more fundamental than quantization procedures. In such an approach the quantum mechanical laws should emerge from the geometrical theory. A toy model that incorporates the idea is presented and its necessary formulation in configuration space is emphasized.Comment: Talk given at QTRF 5 conference, 5 pages, typos corrected, reference adde

Exact renormalization group with optimal scale and its application to cosmology

Assuming an effective gravitational action with scale dependent coupling constants, a consistency condition for the local form of the cut-off scale is derived. The approach is applied to homogeneous cosmology and running couplings with an ultraviolet fixed point. Within the given approach this allows to derive bounds on the value of the fixed point.Comment: 11 pages, 3 figure

The stepwise path integral of the relativistic point particle

In this paper we present a stepwise construction of the path integral over relativistic orbits in Euclidean spacetime. It is shown that the apparent problems of this path integral, like the breakdown of the naive Chapman-Kolmogorov relation, can be solved by a careful analysis of the overcounting associated with local and global symmetries. Based on this, the direct calculation of the quantum propagator of the relativistic point particle in the path integral formulation results from a simple and purely geometric construction.Comment: 10 pages, 5 figure