591 research outputs found
Action functionals of single scalar fields and arbitrary--weight gravitational constraints that generate a genuine Lie algebra
We discuss the issue initiated by Kucha\v{r} {\it et al}, of replacing the
usual Hamiltonian constraint by alternative combinations of the gravitational
constraints (scalar densities of arbitrary weight), whose Poisson brackets
strongly vanish and cast the standard constraint-system for vacuum gravity into
a form that generates a true Lie algebra. It is shown that any such
combination---that satisfies certain reality conditions---may be derived from
an action principle involving a single scalar field and a single Lagrange
multiplier with a non--derivative coupling to gravity.Comment: 26 pages, plain TE
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
A nonlinear quantum model of the Friedmann universe
A discussion is given of the quantisation of a physical system with finite
degrees of freedom subject to a Hamiltonian constraint by treating time as a
constrained classical variable interacting with an unconstrained quantum state.
This leads to a quantisation scheme that yields a Schrodinger-type equation
which is in general nonlinear in evolution. Nevertheless it is compatible with
a probabilistic interpretation of quantum mechanics and in particular the
construction of a Hilbert space with a Euclidean norm is possible. The new
scheme is applied to the quantisation of a Friedmann Universe with a massive
scalar field whose dynamical behaviour is investigated numerically.Comment: 11 pages of text + 4 pages for 8 figure
The Dispersion of Newton's Constant: A Transfer Matrix Formulation of Quantum Gravity
A transfer matrix formalism applicable to certain reparametrization invariant
theories, including quantum gravity, is proposed. In this formulation it is
found that every stationary state in quantum gravity satisfies a Wheeler-DeWitt
equation, but each with a different value of the Planck mass; the value
turns out to be proportional to the eigenvalue of the evolution
operator. As a consequence, the fact that the Universe is non-stationary
implies that it is not in an eigenstate of Newton's constant.Comment: 24 pages, plain LaTeX, NBI-HE-93-5
Remarks on the Reduced Phase Space of (2+1)-Dimensional Gravity on a Torus in the Ashtekar Formulation
We examine the reduced phase space of the Barbero-Varadarajan solutions of
the Ashtekar formulation of (2+1)-dimensional general relativity on a torus. We
show that it is a finite-dimensional space due to existence of an infinite
dimensional residual gauge invariance which reduces the infinite-dimensional
space of solutions to a finite-dimensional space of gauge-inequivalent
solutions. This is in agreement with general arguments which imply that the
number of physical degrees of freedom for (2+1)-dimensional Ashtekar gravity on
a torus is finite.Comment: 13 pages, Latex. More details have been included and the expression
for the finite residual gauge transformations has been worked ou
Unitary Theory of Evaporating 2D Black Holes
We study a manifestly unitary formulation of 2d dilaton quantum gravity based
on the reduced phase space quantization. The spacetime metric can be expanded
in a formal power series of the matter energy-momentum tensor operator. This
expansion can be used for calculating the quantum corrections to the classical
black hole metric by evaluating the expectation value of the metric operator in
an appropriate class of the physical states. When the normal ordering in the
metric operator is chosen to be with respect to Kruskal vacuum, the lowest
order semiclassical metric is exactly the one-loop effective action metric
discovered by Bose, Parker and Peleg. The corresponding semiclassical geometry
describes an evaporating black hole which ends up as a remnant. The calculation
of higher order corrections and implications for the black hole fate are
discussed.Comment: LaTex fil
Black hole solutions in 2+1 dimensions
We give circularly symmetric solutions for null fluid collapse in
2+1-dimensional Einstein gravity with a cosmological constant. The fluid
pressure and energy density are related by . The
long time limit of the solutions are black holes whose horizon structures
depend on the value of . The solution is the
Banados-Teitelboim-Zanelli black hole metric in the long time static limit,
while the solutions give other, `hairy' black hole metrics in this limit.Comment: 8 pages, RevTeX (to appear in Phys. Rev. D) References to Mann and
Ross, and Mann, Chan and Chan adde
Field Theory as Free Fall
It is shown that the classical field equations pertaining to gravity coupled
to other bosonic fields are equivalent to a single geodesic equation,
describing the free fall of a point particle in superspace. Some implications
for quantum gravity are discussed.Comment: 18 pages, plain late
Free fields via canonical transformations of matter-coupled 2D dilaton gravity models
It is shown that the 1+1-dimensional matter-coupled Jackiw-Teitelboim model
and the model with an exponential potential can be converted by means of
appropriate canonical transformations into a bosonic string theory propagating
on a flat target space with an indefinite signature. This makes it possible to
consistently quantize these models in the functional Schroedinger
representation thus generalizing recent results on CGHS theory.Comment: 15 pages, Late
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