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

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 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

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

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

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

The Constraints in Spherically Symmetric General Relativity II --- Identifying the Configuration Space: A Moment of Time Symmetry

We continue our investigation of the configuration space of general relativity begun in I (gr-qc/9411009). Here we examine the Hamiltonian constraint when the spatial geometry is momentarily static (MS). We show that MS configurations satisfy both the positive quasi-local mass (QLM) theorem and its converse. We derive an analytical expression for the spatial metric in the neighborhood of a generic singularity. The corresponding curvature singularity shows up in the traceless component of the Ricci tensor. We show that if the energy density of matter is monotonically decreasing, the geometry cannot be singular. A supermetric on the configuration space which distinguishes between singular geometries and non-singular ones is constructed explicitly. Global necessary and sufficient criteria for the formation of trapped surfaces and singularities are framed in terms of inequalities which relate appropriate measures of the material energy content on a given support to a measure of its volume. The strength of these inequalities is gauged by exploiting the exactly solvable piece-wise constant density star as a template.Comment: 50 pages, Plain Tex, 1 figure available from the authors