2,696 research outputs found
The problem of time and gauge invariance in the quantization of cosmological models. I. Canonical quantization methods
The paper is the first of two parts of a work reviewing some approaches to
the problem of time in quantum cosmology, which were put forward last decade,
and which demonstrated their relation to the problems of reparametrization and
gauge invariance of quantum gravity. In the present part we remind basic
features of quantum geometrodynamics and minisuperspace cosmological models,
and discuss fundamental problems of the Wheeler - DeWitt theory. Various
attempts to find a solution to the problem of time are considered in the
framework of the canonical approach. Possible solutions to the problem are
investigated making use of minisuperspace models, that is, systems with a
finite number of degrees of freedom. At the same time, in the last section of
the paper we expand our consideration beyond the minisuperspace approximation
and briefly review promising ideas by Brown and Kuchar, who propose that dust
interacting only gravitationally can be used for time measuring, and the
unitary approach by Barvinsky and collaborators. The latter approach admits
both the canonical and path integral formulations and anticipates the
consideration of recent developments in the path integral approach in the
second part of our work.Comment: 16 pages, to be published in Grav. Cosmo
Comment on the choice of time in a two-component formulation of the Wheeler--DeWitt equation
The two-component formalism in quantum cosmology is revisited with a
particular emphasis on the identification of time. Its relation with the
appearance of imaginary eigenvalues is established. It is explicitly shown how
a good choice of the global time prevents this peculiarity.Comment: 8 pages; version accepted for publication in Int. J. Mod. Phys.
Gauge fixation and global phase time for minisuperspaces
Homogeneous and isotropic cosmological models whose Hamilton-Jacobi equation is separable are deparametrized by turning their action functional into that of an ordinary gauge system. Canonical gauge conditions imposed on the gauge system are used to define a global phase time in terms of the canonical coordinates and momenta of the minisuperspaces. The procedure clearly shows how the geometry of the constraint surface restricts the choice of time; the consequences that this has on the path integral quantization are discussed
Renormalized Stress Tensor for trans-Planckian Cosmology
Finite expressions for the mean value of the stress tensor corresponding to a
scalar field with a generalized dispersion relation in a
Friedman--Robertson--Walker universe are obtained using adiabatic
renormalization. Formally divergent integrals are evaluated by means of
dimensional regularization. The renormalization procedure is shown to be
equivalent to a redefinition of the cosmological constant and the Newton
constant in the semiclassical Einstein equations.Comment: 14 pages. Minor changes; version published in Physical Review
Probing global aspects of a geometry by the self-force on a charge: Spherical thin-shell wormholes
The self-interaction for a static point charge in the space-time of a
thin-shell wormhole constructed connecting two identical Schwarzschild
geometries is calculated in a series expansion. The electrostatic self-force is
evaluated numerically. It is found to be attractive towards the throat except
for some values of the throat radius proximate to the value of the
Schwarzschild horizon for which the force is repulsive or attractive depending
on the position of the charge. The result differs from the self-force in the
space-time of the Schwarzschild black hole, where it is always repulsive from
the center. Although these wormhole and black hole geometries are locally
indistinguishable, the different topologies of both backgrounds are manifested
in the electrostatic field of a point charge.Comment: 17 pages, 4 figue
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