Determination and Reduction of Large Diffeomorphisms

Within the Hamiltonian formulation of diffeomorphism invariant theories we address the problem of how to determine and how to reduce diffeomorphisms outside the identity component.Comment: 4 pages, Latex, macro espcrc2.sty. Contribution to the proceedings of the second conference on Constrained Dynamics and Quantum Gravity, Santa Margherita, Italy, 17-21 September 1996. To appear in Nucl. Phys. B Supp

Group Averaging and Refined Algebraic Quantization

We review the framework of Refined Algebraic Quantization and the method of Group Averaging for quantizing systems with first-class constraints. Aspects and results concerning the generality, limitations, and uniqueness of these methods are discussed.Comment: 4 pages, LaTeX 2.09 using espcrc2.sty. To appear in the proceedings of the third "Meeting on Constrained Dynamics and Quantum Gravity", Nucl. Phys. B (Proc. Suppl.

Two black hole initial data

Misner initial data are a standard example of time-symmetric initial data with two apparent horizons. Compact formulae describing such data are presented in the cases of equal or non-equal masses (i.e. isometric or non-isometric horizons). The interaction energy in the "Schwarzschild + test particle" limit of the Misner data is analyzed.Comment: 4 pages, RevTeX4, journal version, a reference added, minor correction

On the origin of probability in quantum mechanics

I give a brief introduction to many worlds or "no wavefunction collapse" quantum mechanics, suitable for non-specialists. I then discuss the origin of probability in such formulations, distinguishing between objective and subjective notions of probability.Comment: 7 pages, 2 figures. This version to appear as a Brief Review in Modern Physics Letter

The Canonical Approach to Quantum Gravity: General Ideas and Geometrodynamics

We give an introduction to the canonical formalism of Einstein's theory of general relativity. This then serves as the starting point for one approach to quantum gravity called quantum geometrodynamics. The main features and applications of this approach are briefly summarized.Comment: 21 pages, 6 figures. Contribution to E. Seiler and I.-O. Stamatescu (editors): `Approaches To Fundamental Physics -- An Assessment Of Current Theoretical Ideas' (Springer Verlag, to appear

Consistency of Semiclassical Gravity

We discuss some subtleties which arise in the semiclassical approximation to quantum gravity. We show that integrability conditions prevent the existence of Tomonaga-Schwinger time functions on the space of three-metrics but admit them on superspace. The concept of semiclassical time is carefully examined. We point out that central charges in the matter sector spoil the consistency of the semiclassical approximation unless the full quantum theory of gravity and matter is anomaly-free. We finally discuss consequences of these considerations for quantum field theory in flat spacetime, but with arbitrary foliations.Comment: 12 pages, LATEX, Report Freiburg THEP-94/2

Hawking radiation from decoherence

It is argued that the thermal nature of Hawking radiation arises solely due to decoherence. Thereby any information-loss paradox is avoided because for closed systems pure states remain pure. The discussion is performed for a massless scalar field in the background of a Schwarzschild black hole, but the arguments should hold in general. The result is also compared to and contrasted with the situation in inflationary cosmology.Comment: 6 pages, to appear in Class. Quantum Gra

Quantum Zeno Effect for Exponentially Decaying Systems

The quantum Zeno effect -- suppression of decay by frequent measurements -- was believed to occur only when the response of the detector is so quick that the initial tiny deviation from the exponential decay law is detectable. However, we show that it can occur even for exactly exponentially decaying systems, for which this condition is never satisfied, by considering a realistic case where the detector has a finite energy band of detection. The conventional theories correspond to the limit of an infinite bandwidth. This implies that the Zeno effect occurs more widely than expected so far.Comment: 4 pages, 3 figure

Decoherence in a system of many two--level atoms

I show that the decoherence in a system of $N$ degenerate two--level atoms interacting with a bosonic heat bath is for any number of atoms $N$ governed by a generalized Hamming distance (called ``decoherence metric'') between the superposed quantum states, with a time--dependent metric tensor that is specific for the heat bath.The decoherence metric allows for the complete characterization of the decoherence of all possible superpositions of many-particle states, and can be applied to minimize the over-all decoherence in a quantum memory. For qubits which are far apart, the decoherence is given by a function describing single-qubit decoherence times the standard Hamming distance. I apply the theory to cold atoms in an optical lattice interacting with black body radiation.Comment: replaced with published versio