Probing the small distance structure of canonical quantum gravity using the conformal group

In canonical quantum gravity, the formal functional integral includes an integration over the local conformal factor, and we propose to perform the functional integral over this factor before doing any of the other functional integrals. By construction, the resulting effective theory would be expected to be conformally invariant and therefore finite. However, also the conformal integral itself diverges, and the effects of a renormalization counter term are considered. It generates problems such as unitarity violation, due to a Landau-like ghost, and conformal anomalies. Adding (massive or massless) matter fields does not change the picture. Various alternative ideas are offered, including a more daring speculation, which is that no counter term should be allowed for at all. This has far-reaching and important consequences, which we discuss. A surprising picture emerges of quantized elementary particles interacting with a gravitational field, in particular gravitons, which are "partly classical". This approach was inspired by a search towards the reconciliation of Hawking radiation with unitarity and locality, and it offers basic new insights there.Comment: 22 pages (incl. title page), 1 figure. Substantial changes in the discussion sections, minor errors corrected, and references adde

Confinement at Large Nc

A discussion is given of the confinement mechanism in terms of the Abelian projection scheme, for a general number Nc of colors. There is a difficulty in the Nc to infinity limit that requires a careful treatment, as the charges of the condensing magnetic monopoles tend to infinity. We suggest that Bose condensation of electric or magnetic charges is indicative for the kind of confinement that takes place, but the actual mechanism of confinement depends on other features as well.Comment: 11 pages, 3 figures. Presented at "Large N QCD", trento, July 200

Canonical Quantization of Gravitating Point Particles in 2+1 Dimensions

A formalism previously introduced by the author using tesselated Cauchy surfaces is applied to define a quantized version of gravitating point particles in 2+1 dimensions. We observe that this is the first model whose quantum version automatically discretizes time. But also spacelike distances are discretized in a very special way.Comment: 14 pages (TeX), 3 figures (Postscript), Utrecht THU-93/1

The Grand View of Physics

Abdus Salam was known for his `grand views', grand views of science as well as grand views of society. In this talk the grand view of theoretical physics is put in perspective.Comment: 5 pages, 1 figure. Presented at Salam +50, Imperial College, London, July 7, 200