629 research outputs found
Gravitational Constraint Combinations Generate a Lie Algebra
We find a first--order partial differential equation whose solutions are all
ultralocal scalar combinations of gravitational constraints with Abelian
Poisson brackets between themselves. This is a generalisation of the Kucha\v{r}
idea of finding alternative constraints for canonical gravity. The new scalars
may be used in place of the hamiltonian constraint of general relativity and,
together with the usual momentum constraints, replace the Dirac algebra for
pure gravity with a true Lie algebra: the semidirect product of the Abelian
algebra of the new constraint combinations with the algebra of spatial
diffeomorphisms.Comment: 10 pages, latex, submitted to Classical and Quantum Gravity. Section
3 is expanded and an additional solution provided, minor errors correcte
Canonical Equivalence of a Generic 2D Dilaton Gravity Model and a Bosonic String Theory
We show that a canonical tranformation converts, up to a boundary term, a
generic 2d dilaton gravity model into a bosonic string theory with a
Minkowskian target space.Comment: LaTeX file, 9 pages, no figure
Quanta Without Quantization
The dimensional properties of fields in classical general relativity lead to
a tangent tower structure which gives rise directly to quantum mechanical and
quantum field theory structures without quantization. We derive all of the
fundamental elements of quantum mechanics from the tangent tower structure,
including fundamental commutation relations, a Hilbert space of pure and mixed
states, measurable expectation values, Schroedinger time evolution, collapse of
a state and the probability interpretation. The most central elements of string
theory also follow, including an operator valued mode expansion like that in
string theory as well as the Virasoro algebra with central charges.Comment: 8 pages, Latex, Honorable Mention 1997 GRG Essa
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
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
Canonical Formulation of pp-waves
We construct a Hamiltonian formulation for the class of plane-fronted
gravitational waves with parallel rays (pp-waves). Because of the existence of
a light-like Killing vector, the dynamics is effectively reduced to a 2+1
evolution with "time" chosen to be light-like. In spite of the vanishing action
this allows us to geometrically identify a symplectic form as well as dynamical
Hamiltonian, thus casting the system into canonical form.Comment: To appear in the "Obregon Festschrift
Free Field Realization of Cylindrically Symmetric Einstein Gravity
Cylindrically reduced Einstein gravity can be regarded as an
sigma model coupled to 2D dilaton gravity. By using the corresponding 2D
diffeomorphism algebra of constraints and the asymptotic behaviour of the Ernst
equation we show that the theory can be mapped by a canonical transformation
into a set of free fields with a Minkowskian target space. We briefly discuss
the quantization in terms of these free-field variables, which is considerably
simpler than in the other approaches.Comment: 8 pages, no figures, discussions on the dual metric and on the
free-field expansion are 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
General relativity histories theory II: Invariance groups
We show in detail how the histories description of general relativity carries
representations of both the spacetime diffeomorphisms group and the Dirac
algebra of constraints. We show that the introduction of metric-dependent
equivariant foliations leads to the crucial result that the canonical
constraints are invariant under the action of spacetime diffeomorphisms.
Furthermore, there exists a representation of the group of generalised
spacetime mappings that are functionals of the four-metric: this is a spacetime
analogue of the group originally defined by Bergmann and Komar in the context
of the canonical formulation of general relativity. Finally, we discuss the
possible directions for the quantization of gravity in histories theory.Comment: 24 pages, submitted to Class. Quant. Gra
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