112 research outputs found
On the relation between 2+1 Einstein gravity and Chern Simons theory
A simple example is given to show that the gauge equivalence classes of
physical states in Chern Simons theory are not in one-to-one correspondence
with those of Einstein gravity in three spacetime dimensions. The two theories
are therefore not equivalent. It is shown that including singular metrics into
general relativity has more, and in fact a quite counter-intuitive, impact on
the theory than one naively expects.Comment: 14 pages, LaTeX2e, 3 eps figure
New representation and a vacuum state for canonical quantum gravity
A new representation for canonical gravity and supergravity is presented,
which combines advantages of Ashtekar's and the Wheeler~DeWitt representation:
it has a nice geometric structure and the singular metric problem is absent. A
formal state functional can be given, which has some typical features of a
vacuum state in quantum field theory. It can be canonically transformed into
the metric representation. Transforming the constraints too, one recovers the
Wheeler~DeWitt equation up to an anomalous term. A modified Dirac quantization
is proposed to handle possible anomalies in the constraint algebra.Comment: 28 pages, LaTe
The 2+1 Kepler Problem and Its Quantization
We study a system of two pointlike particles coupled to three dimensional
Einstein gravity. The reduced phase space can be considered as a deformed
version of the phase space of two special-relativistic point particles in the
centre of mass frame. When the system is quantized, we find some possibly
general effects of quantum gravity, such as a minimal distances and a foaminess
of the spacetime at the order of the Planck length. We also obtain a
quantization of geometry, which restricts the possible asymptotic geometries of
the universe.Comment: 59 pages, LaTeX2e, 9 eps figure
Physical States in d=3,N=2 Supergravity
To clarify some issues raised by D'Eath's recent proposal for the physical
states of supergravity in four dimensions, we study pure (topological)
supergravity in three dimensions, which is formally very similar, but
much easier to solve. The wave functionals solving the quantum constraints can
be understood in terms of arbitrary functions on the space of moduli and
supermoduli, which is not Hausdorff. We discuss the implications for the wave
functionals and show that these are not amenable to expansions in fermionic
coordinates, but can serve as lowest-order solutions to the quantum constraints
in an expansion in in more realistic theories.Comment: 11 pages, Report DESY 93-125, THU-93/1
The Phase Space Structure of Multi Particle Models in 2+1 Gravity
What can we learn about quantum gravity from a simple toy model, without
actually quantizing it? The toy model consists of a finite number of point
particles, coupled to three dimensional Einstein gravity. It has finitely many
physical degrees of freedom. These are basically the relative positions of the
particles in spacetime and the conjugate momenta. The resulting reduced phase
space is derived from Einstein gravity as a topological field theory. The
crucial point is thereby that we do not make any a priori assumptions about
this phase space, except that the dynamics of the gravitational field is
defined by the Einstein Hilbert action. This already leads to some interesting
features of the reduced phase space, such as a non-commutative structure of
spacetime when the model is quantized.Comment: 72 pages, LeTeX2e, 10 eps figure
The Anti-de Sitter Gott Universe: A Rotating BTZ Wormhole
Recently it has been shown that a 2+1 dimensional black hole can be created
by a collapse of two colliding massless particles in otherwise empty anti-de
Sitter space. Here we generalize this construction to the case of a non-zero
impact parameter. The resulting spacetime, which may be regarded as a Gott
universe in anti-de Sitter background, contains closed timelike curves. By
treating these as singular we are able to interpret our solution as a rotating
black hole, hence providing a link between the Gott universe and the BTZ black
hole. When analyzing the spacetime we see how the full causal structure of the
interior can be almost completely inferred just from considerations of the
conformal boundary.Comment: 46 pages (LaTeX2e), 13 figures (eps
Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity
We study the phase space structure and the quantization of a pointlike
particle in 2+1 dimensional gravity. By adding boundary terms to the first
order Einstein Hilbert action, and removing all redundant gauge degrees of
freedom, we arrive at a reduced action for a gravitating particle in 2+1
dimensions, which is invariant under Lorentz transformations and a group of
generalized translations. The momentum space of the particle turns out to be
the group manifold SL(2). Its position coordinates have non-vanishing Poisson
brackets, resulting in a non-commutative quantum spacetime. We use the
representation theory of SL(2) to investigate its structure. We find a
discretization of time, and some semi-discrete structure of space. An
uncertainty relation forbids a fully localized particle. The quantum dynamics
is described by a discretized Klein Gordon equation.Comment: 58 pages, 3 eps figures, presentation of the classical theory
improve
- …