1,729 research outputs found

### 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

### 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

### Existence of Spinorial States in Pure Loop Quantum Gravity

We demonstrate the existence of spinorial states in a theory of canonical
quantum gravity without matter. This should be regarded as evidence towards the
conjecture that bound states with particle properties appear in association
with spatial regions of non-trivial topology. In asymptotically trivial general
relativity the momentum constraint generates only a subgroup of the spatial
diffeomorphisms. The remaining diffeomorphisms give rise to the mapping class
group, which acts as a symmetry group on the phase space. This action induces a
unitary representation on the loop state space of the Ashtekar formalism.
Certain elements of the diffeomorphism group can be regarded as asymptotic
rotations of space relative to its surroundings. We construct states that
transform non-trivially under a $2\pi$-rotation: gravitational quantum states
with fractional spin.Comment: 26 pages, 6 figures. Changes made to section 2 and Lemma

### An Analysis of the Representations of the Mapping Class Group of a Multi-Geon Three-Manifold

It is well known that the inequivalent unitary irreducible representations
(UIR's) of the mapping class group $G$ of a 3-manifold give rise to ``theta
sectors'' in theories of quantum gravity with fixed spatial topology. In this
paper, we study several families of UIR's of $G$ and attempt to understand the
physical implications of the resulting quantum sectors. The mapping class group
of a three-manifold which is the connected sum of $\R^3$ with a finite number
of identical irreducible primes is a semi-direct product group. Following
Mackey's theory of induced representations, we provide an analysis of the
structure of the general finite dimensional UIR of such a group. In the picture
of quantized primes as particles (topological geons), this general
group-theoretic analysis enables one to draw several interesting qualitative
conclusions about the geons' behavior in different quantum sectors, without
requiring an explicit knowledge of the UIR's corresponding to the individual
primes.Comment: 52 pages, harvmac, 2 postscript figures, epsf required. Added an
appendix proving the semi-direct product structure of the MCG, corrected an
error in the characterization of the slide subgroup, reworded extensively.
All our analysis and conclusions remain as befor

### 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

### 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

### On Doppler tracking in cosmological spacetimes

We give a rigorous derivation of the general-relativistic formula for the
two-way Doppler tracking of a spacecraft in Friedmann-Lemaitre-Robertson-Walker
and in McVittie spacetimes. The leading order corrections of the so-determined
acceleration to the Newtonian acceleration are due to special-relativistic
effects and cosmological expansion. The latter, although linear in the Hubble
constant, is negligible in typical applications within the Solar System.Comment: 10 pages, 1 figure. Journal versio

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