127 research outputs found
Quantization of generally covariant systems with extrinsic time
A generally covariant system can be deparametrized by means of an
``extrinsic'' time, provided that the metric has a conformal ``temporal''
Killing vector and the potential exhibits a suitable behavior with respect to
it. The quantization of the system is performed by giving the well ordered
constraint operators which satisfy the algebra. The searching of these
operators is enlightned by the methods of the BRST formalism.Comment: 10 pages. Definite published versio
Revised Canonical Quantum Gravity via the Frame Fixing
We present a new reformulation of the canonical quantum geometrodynamics,
which allows to overcome the fundamental problem of the frozen formalism and,
therefore, to construct an appropriate Hilbert space associate to the solution
of the restated dynamics. More precisely, to remove the ambiguity contained in
the Wheeler-DeWitt approach, with respect to the possibility of a (3 +
1)-splitting when the space-time is in a quantum regime, we fix the reference
frame (i.e. the lapse function and the shift vector) by introducing the
so-called kinematical action; as a consequence the new super-Hamiltonian
constraint becomes a parabolic one and we arrive to a Schroedinger-like
approach for the quantum dynamics. In the semiclassical limit our theory
provides General Relativity in the presence of an additional energy-momentum
density contribution coming from no longer zero eigenvalues of the Hamiltonian
constraints; the interpretation of these new contributions comes out in natural
way as soon as it is recognized that the kinematical action can be recasted in
such a way it describes a pressureless, but, in general, non geodesic perfect
fluid.Comment: 24 pages, 0 figures, to appear on Int. Jour. Mod. Phys.
Covariant perturbations of domain walls in curved spacetime
A manifestly covariant equation is derived to describe the perturbations in a
domain wall on a given background spacetime. This generalizes recent work on
domain walls in Minkowski space and introduces a framework for examining the
stability of relativistic bubbles in curved spacetimes.Comment: 15 pages,ICN-UNAM-93-0
Dust as a Standard of Space and Time in Canonical Quantum Gravity
The coupling of the metric to an incoherent dust introduces into spacetime a
privileged dynamical reference frame and time foliation. The comoving
coordinates of the dust particles and the proper time along the dust worldlines
become canonical coordinates in the phase space of the system. The Hamiltonian
constraint can be resolved with respect to the momentum that is canonically
conjugate to the dust time. Imposition of the resolved constraint as an
operator restriction on the quantum states yields a functional Schr\"{o}dinger
equation. The ensuing Hamiltonian density has an extraordinary feature: it
depends only on the geometric variables, not on the dust coordinates or time.
This has three important consequences. First, the functional Schr\"{o}dinger
equation can be solved by separating the dust time from the geometric
variables. Second, the Hamiltonian densities strongly commute and therefore can
be simultaneously defined by spectral analysis. Third, the standard constraint
system of vacuum gravity is cast into a form in which it generates a true Lie
algebra. The particles of dust introduce into space a privileged system of
coordinates that allows the supermomentum constraint to be solved explicitly.
The Schr\"{o}dinger equation yields a conserved inner product that can be
written in terms of either the instantaneous state functionals or the solutions
of constraints. Examples of gravitational observables are given, though neither
the intrinsic metric nor the extrinsic curvature are observables. Disregarding
factor--ordering difficulties, the introduction of dust provides a satisfactory
phenomenological approach to the problem of time in canonical quantum gravity.Comment: 56 pages (REVTEX file + 3 postscipt figure files
A Kucha\v{r} Hypertime Formalism For Cylindrically Symmetric Spacetimes With Interacting Scalar Fields
The Kucha\v{r} canonical transformation for vacuum geometrodynamics in the
presence of cylindrical symmetry is applied to a general non-vacuum case. The
resulting constraints are highly non-linear and non-local in the momenta
conjugate to the Kucha\v{r} embedding variables. However, it is demonstrated
that the constraints can be solved for these momenta and thus the dynamics of
cylindrically symmetric models can be cast in a form suitable for the
construction of a hypertime functional Schr\"odinger equation.Comment: 5 pages, LaTeX, UBCTP-93-02
Dirac Constraint Quantization of a Dilatonic Model of Gravitational Collapse
We present an anomaly-free Dirac constraint quantization of the
string-inspired dilatonic gravity (the CGHS model) in an open 2-dimensional
spacetime. We show that the quantum theory has the same degrees of freedom as
the classical theory; namely, all the modes of the scalar field on an auxiliary
flat background, supplemented by a single additional variable corresponding to
the primordial component of the black hole mass. The functional Heisenberg
equations of motion for these dynamical variables and their canonical
conjugates are linear, and they have exactly the same form as the corresponding
classical equations. A canonical transformation brings us back to the physical
geometry and induces its quantization.Comment: 37 pages, LATEX, no figures, submitted to Physical Review
Cosmological Time in Quantum Supergravity
The version of supergravity formulated by Ogievetsky and Sokatchev is almost
identical to the conventional theory, except that the cosmological
constant appears as a dynamical variable which is constant only by
virtue of the field equations. We consider the canonical quantisation of this
theory, and show that the wave function evolves with respect to a dynamical
variable which can be interpreted as a cosmological time parameter. The square
of the modulus of the wave function obeys a set of simple conservation
equations and can be interpreted as a probability density functional. The usual
problems associated with time in quantum gravity are avoided.Comment: 12 pages, LaTe
Relativistic Solenoids
We construct a general relativistic analogy of an infinite solenoid, i.e., of
an infinite cylinder with zero electric charge and non-zero electric current in
the direction tangential to the cylinder and perpendicular to its axis. We
further show that the solution has a good weak-field limit.Comment: 9 pages, 2 figure
Constraints in Quantum Geometrodynamics
We compare different treatments of the constraints in canonical quantum
gravity. The standard approach on the superspace of 3--geometries treats the
constraints as the sole carriers of the dynamic content of the theory, thus
rendering the traditional dynamical equations obsolete. Quantization of the
constraints in both the Dirac and ADM square root Hamiltonian approaches leads
to the well known problems of time evolution. These problems of time are of
both an interpretational and technical nature. In contrast, the geometrodynamic
quantization procedure on the superspace of the true dynamical variables
separates the issues of quantization from the enforcement of the constraints.
The resulting theory takes into account states that are off-shell with respect
to the constraints, and thus avoids the problems of time. We develop, for the
first time, the geometrodynamic quantization formalism in a general setting and
show that it retains all essential features previously illustrated in the
context of homogeneous cosmologies.Comment: 36 pages, no figures, submitted to IJMPA, Rewording, Fixed Typo
On Unitary Time Evolution in Gowdy Cosmologies
A non-perturbative canonical quantization of Gowdy polarized models
carried out recently is considered. This approach profits from the equivalence
between the symmetry reduced model and 2+1 gravity coupled to a massless real
scalar field. The system is partially gauge fixed and a choice of internal time
is performed, for which the true degrees of freedom of the model reduce to a
massless free scalar field propagating on a 2-dimensional expanding torus. It
is shown that the symplectic transformation that determines the classical
dynamics cannot be unitarily implemented on the corresponding Hilbert space of
quantum states. The implications of this result for both quantization of fields
on curved manifolds and physically relevant questions regarding the initial
singularity are discussed.Comment: 16 pages, no figures, latex file; references added, a proof included.
Final version to appear in IJMP
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