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

Geometric Bounds in Spherically Symmetric General Relativity

We exploit an arbitrary extrinsic time foliation of spacetime to solve the constraints in spherically symmetric general relativity. Among such foliations there is a one parameter family, linear and homogeneous in the extrinsic curvature, which permit the momentum constraint to be solved exactly. This family includes, as special cases, the extrinsic time gauges that have been exploited in the past. These foliations have the property that the extrinsic curvature is spacelike with respect to the the spherically symmetric superspace metric. What is remarkable is that the linearity can be relaxed at no essential extra cost which permits us to isolate a large non - pathological dense subset of all extrinsic time foliations. We identify properties of solutions which are independent of the particular foliation within this subset. When the geometry is regular, we can place spatially invariant numerical bounds on the values of both the spatial and the temporal gradients of the scalar areal radius, $R$. These bounds are entirely independent of the particular gauge and of the magnitude of the sources. When singularities occur, we demonstrate that the geometry behaves in a universal way in the neighborhood of the singularity.Comment: 16 pages, revtex, submitted to Phys. Rev.

Time reparameterization in Bianchi type I spinor cosmology

The problem of time reparameterization is addressed at both the classical and quantum levels in a Bianchi-I universe in which the matter source is a massive Dirac spinor field. We take the scale factors of the metric as the intrinsic time and their conjugate momenta as the extrinsic time. A scalar character of the spinor field is identified as a representation of the extrinsic time. The construction of the field equations and quantization of the model is achieved by solving the Hamiltonian constraint after time identification has been dealt with. This procedure leads to a true Hamiltonian whose exact solutions for the above choices of time are presentedComment: 16 pages, no figures, to appear in Annals of Physic

Selection rules for the Wheeler-DeWitt equation in quantum cosmology

Selection of physically meaningful solutions of the Wheeler-DeWitt equation for the wavefunction in quantum cosmology, can be attained by a reduction of the theory to the sector of true physical degrees of freedom and their canonical quantization. The resulting physical wavefunction unitarily evolving in the time variable introduced within this reduction can then be raised to the level of the cosmological wavefunction in superspace of 3-metrics. We apply this technique in several simple minisuperspace models and discuss both at classical and quantum level physical reduction in {\em extrinsic} time -- the time variable determined in terms of extrinsic curvature. Only this extrinsic time gauge can be consistently used in vicinity of turning points and bounces where the scale factor reaches extremum. Since the 3-metric scale factor is canonically dual to extrinsic time variable, the transition from the physical wavefunction to the wavefunction in superspace represents a kind of the generalized Fourier transform. This transformation selects square integrable solutions of the Wheeler-DeWitt equation, which guarantee Hermiticity of canonical operators of the Dirac quantization scheme. Semiclassically this means that wavefunctions are represented by oscillating waves in classically allowed domains of superspace and exponentially fall off in classically forbidden (underbarrier) regions. This is explicitly demonstrated in flat FRW model with a scalar field having a constant negative potential and for the case of phantom scalar field with a positive potential. The FRW model of a scalar field with a vanishing potential does not lead to selection rules for solutions of the Wheeler-DeWitt equation, but this does not violate Hermiticity properties, because all these solutions are anyway of plane wave type and describe cosmological dynamics without turning points and bounces.Comment: final version, to appear in Physical Review

Two-dimensional dilaton gravity in a unitary gauge

Reduced phase space formulation of CGHS model of 2d dilaton gravity is studied in en extrinsic time gauge. The corresponding Hamiltonian can be promoted into a Hermitian operator acting in the physical Hilbert space, implying a unitary evolution for the system. Consequences for the black hole physics are discussed. In particular, this manifestly unitary theory rules out the Hawking scenario for the endpoint of the black hole evaporation process.Comment: 12 pages, LaTex file, Imperial-TP/92-93/8 and QMW/PH/92/1

Ashtekar Formulation of 2+1 Gravity on a Torus

Pure (2+1)-dimensional Einstein gravity is analysed in the Ashtekar formulation, when the spatial manifold is a torus. We have found a set of globally defined observables, forming a closed algebra. This allowed us to solve the quantum constraints, and to show that the reduced phase space of the Ashtekar formulation is greater then the corresponding space of the Witten formulation. Furthermore, we have found a globally defined time variable which satisfies all the requiriments of an extrinsic time variable in quantum gravity.Comment: 15 page

Entropic sampling dynamics of the globally-coupled kinetic Ising model

The entropic sampling dynamics based on the reversible information transfer to and from the environment is applied to the globally coupled Ising model in the presence of an oscillating magnetic field. When the driving frequency is low enough, coherence between the magnetization and the external magnetic field is observed; such behavior tends to weaken with the system size. The time-scale matching between the intrinsic time scale, defined in the absence of the external magnetic field, and the extrinsic time scale, given by the inverse of the driving frequency, is used to explain the observed coherence behavior.Comment: 8 page