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 Free-Will Postulate in Quantum Mechanics

The so-called "free will axiom" is an essential ingredient in many discussions concerning hidden variables in quantum mechanics. In this paper we argue that "free will" can be defined in different ways. The definition usually employed is clearly invalid in strictly deterministic theories. A different, more precise formulation is proposed here, defining a condition that may well be a more suitable one to impose on theoretical constructions and models. Our axiom, to be referred to as the `unconstrained initial state' condition, has consequences similar to "free will", but does not clash with determinism, and appears to lead to different conclusions concerning causality and locality in quantum mechanics. Models proposed earlier by this author fall in this category. Imposing our `unconstrained initial state' condition on a deterministic theory underlying Quantum Mechanics, appears to lead to a restricted free-will condition in the quantum system: an observer has the free will to modify the setting of a measuring device, but has no control over the phase of its wave function. The dismissal of the usual "free will" concept does not have any consequences for our views and interpretations of human activities in daily life, and the way our minds function, but it requires a more careful discussion on what, in practice, free will actually amounts to.Comment: 8 pages, 1 figur

The Conformal Constraint in Canonical Quantum Gravity

Perturbative canonical quantum gravity is considered, when coupled to a renormalizable model for matter fields. It is proposed that the functional integral over the dilaton field should be disentangled from the other integrations over the metric fields. This should generate a conformally invariant theory as an intermediate result, where the conformal anomalies must be constrained to cancel out. When the residual metric is treated as a background, and if this background is taken to be flat, this leads to a novel constraint: in combination with the dilaton contributions, the matter lagrangian should have a vanishing beta function. The zeros of this beta function are isolated points in the landscape of quantum field theories, and so we arrive at a denumerable, or perhaps even finite, set of quantum theories for matter, where not only the coupling constants, but also the masses and the cosmological constant are all fixed, and computable, in terms of the Planck units