466 research outputs found
Dirac Quantization of Two-Dimensional Dilaton Gravity Minimally Coupled to N Massless Scalar Fields
It is shown that the Callan-Giddings-Harvey-Strominger theory on the cylinder
can be consistently quantized (using Dirac's approach) without imposing any
constraints on the sign of the gravitational coupling constant or the sign (or
value) of the cosmological constant. The quantum constraints in terms of the
original geometrical variables are also derived
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
Minisuperspace Model for Revised Canonical Quantum Gravity
We present a reformulation of the canonical quantization of gravity, as
referred to the minisuperspace; the new approach is based on fixing a Gaussian
(or synchronous) reference frame and then quantizing the system via the
reconstruction of a suitable constraint; then the quantum dynamics is re-stated
in a generic coordinates system and it becomes dependent on the lapse function.
The analysis follows a parallelism with the case of the non-relativistic
particle and leads to the minisuperspace implementation of the so-called {\em
kinematical action} as proposed in \cite{M02} (here almost coinciding also with
the approach presented in \cite{KT91}). The new constraint leads to a
Schr\"odinger equation for the system. i.e. to non-vanishing eigenvalues for
the super-Hamiltonian operator; the physical interpretation of this feature
relies on the appearance of a ``dust fluid'' (non-positive definite) energy
density, i.e. a kind of ``materialization'' of the reference frame. As an
example of minisuperspace model, we consider a Bianchi type IX Universe, for
which some dynamical implications of the revised canonical quantum gravity are
discussed. We also show how, on the classical limit, the presence of the dust
fluid can have relevant cosmological issues. Finally we upgrade our analysis by
its extension to the generic cosmological solution, which is performed in the
so-called long-wavelength approximation. In fact, near the Big-Bang, we can
neglect the spatial gradients of the dynamical variables and arrive to
implement, in each space point, the same minisuperspace paradigm valid for the
Bianchi IX model.Comment: 16 pages, no figures, to appear on International Journal of Modern
Physics
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 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
ADM Worldvolume Geometry
We describe the dynamics of a relativistic extended object in terms of the
geometry of a configuration of constant time. This involves an adaptation of
the ADM formulation of canonical general relativity. We apply the formalism to
the hamiltonian formulation of a Dirac-Nambu-Goto relativistic extended object
in an arbitrary background spacetime.Comment: 4 pages, Latex. Uses espcrc2.sty To appear in the proceedings of the
Third Conference on Constrained Dynamics and Quantum Gravity, September,
1999. To appear in Nuclear Physics B (Proceedings Supplement
Free-Field Realization of D-dimensional Cylindrical Gravitational Waves
We find two-dimensional free-field variables for D-dimensional general
relativity on spacetimes with D-2 commuting spacelike Killing vector fields and
non-compact spatial sections for D>4. We show that there is a canonical
transformation which maps the corresponding two-dimensional dilaton gravity
theory into a two-dimensional diffeomorphism invariant theory of the free-field
variables. We also show that the spacetime metric components can be expressed
as asymptotic series in negative powers of the dilaton, with coefficients which
can be determined in terms of the free fields.Comment: 15 pages, Late
Time asymmetries in quantum cosmology and the searching for boundary conditions to the Wheeler-DeWitt equation
The paper addresses the quantization of minisuperspace cosmological models by
studying a possible solution to the problem of time and time asymmetries in
quantum cosmology. Since General Relativity does not have a privileged time
variable of the newtonian type, it is necessary, in order to have a dynamical
evolution, to select a physical clock. This choice yields, in the proposed
approach, to the breaking of the so called clock-reversal invariance of the
theory which is clearly distinguished from the well known motion-reversal
invariance of both classical and quantum mechanics. In the light of this new
perspective, the problem of imposing proper boundary conditions on the space of
solutions of the Wheeler-DeWitt equation is reformulated. The symmetry-breaking
formalism of previous papers is analyzed and a clarification of it is proposed
in order to satisfy the requirements of the new interpretation.Comment: 25 pages, 1 figur
Brane-world Quantum Gravity
The Arnowitt-Deser-Misner canonical formulation of general relativity is
extended to the covariant brane-world theory in arbitrary dimensions. The
exclusive probing of the extra dimensions makes a substantial difference,
allowing for the construction of a non-constrained canonical theory. The
quantum states of the brane-world geometry are defined by the
Tomonaga-Schwinger equation, whose integrability conditions are determined by
the classical perturbations of submanifolds contained in the Nash's
differentiable embedding theorem. In principle, quantum brane-world theory can
be tested by current experiments in astrophysics and by near future laboratory
experiments at Tev energy. The implications to the black-hole information loss
problem, to the accelerating cosmology, and to a quantum mathematical theory of
four-sub manifolds are briefly commented.Comment: 14 pages, no figures, JHEP format, to appear in JHEP April 200
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