9 research outputs found
Unitary evolution of free massless fields in de Sitter space-time
We consider the quantum dynamics of a massless scalar field in de Sitter
space-time. The classical evolution is represented by a canonical
transformation on the phase space for the field theory. By studying the
corresponding Bogoliubov transformations, we show that the symplectic map that
encodes the evolution between two instants of time cannot be unitarily
implemented on any Fock space built from a SO(4)-symmetric complex structure.
We will show also that, in contrast with some effectively lower dimensional
examples arising from Quantum General Relativity such as Gowdy models, it is
impossible to find a time dependent conformal redefinition of the massless
scalar field leading to a quantum unitary dynamics.Comment: 20 pages. Comments and references adde
Hamiltonian Dynamics of Linearly Polarized Gowdy Models Coupled to Massless Scalar Fields
The purpose of this paper is to analyze in detail the Hamiltonian formulation
for the compact Gowdy models coupled to massless scalar fields as a necessary
first step towards their quantization. We will pay special attention to the
coupling of matter and those features that arise for the three-handle and
three-sphere topologies that are not present in the well studied three torus
case -in particular the polar constraints that come from the regularity
conditions on the metric. As a byproduct of our analysis we will get an
alternative understanding, within the Hamiltonian framework, of the appearance
of initial and final singularities for these models.Comment: Final version to appear in Classical and Quantum Gravit
Quantum Cylindrical Waves and Sigma Models
We analyze cylindrical gravitational waves in vacuo with general polarization
and develop a viewpoint complementary to that presented recently by Niedermaier
showing that the auxiliary sigma model associated with this family of waves is
not renormalizable in the standard perturbative sense.Comment: 11 pages (DIN A4), accepted in International Journal of Modern
Physics
A Note on the Symmetry Reduction of SU(2) on Horizons of Various Topologies
It is known that the SU(2) degrees of freedom manifest in the description of
the gravitational field in loop quantum gravity are generally reduced to U(1)
degrees of freedom on an isolated horizon. General relativity also allows
black holes with planar, toroidal, or higher genus topology for their horizons.
These solutions also meet the criteria for an isolated horizon, save for the
topological criterion, which is not crucial. We discuss the relevant
corresponding symmetry reduction for black holes of various topologies (genus 0
and ) here and discuss its ramifications to black hole entropy within
the loop quantum gravity paradigm. Quantities relevant to the horizon theory
are calculated explicitly using a generalized ansatz for the connection and
densitized triad, as well as utilizing a general metric admitting hyperbolic
sub-spaces. In all scenarios, the internal symmetry may be reduced to
combinations of U(1).Comment: 13 pages, two figures. Version 2 has several references updated and
added, as well as some minor changes to the text. Accepted for publication in
Class. Quant. Gra