13 research outputs found
Integrable Classical and Quantum Gravity
In these lectures we report recent work on the exact quantization of
dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space
sigma-models coupled to gravity and a dilaton. Using methods developed in the
context of flat space integrable systems, the Wheeler-DeWitt equations for
these models can be reduced to a modified version of the Knizhnik-Zamolodchikov
equations from conformal field theory, the insertions given by singularities in
the spectral parameter plane. This basic result in principle permits the
explicit construction of solutions, i.e. physical states of the quantized
theory. In this way, we arrive at integrable models of quantum gravity with
infinitely many self-interacting propagating degrees of freedom.Comment: 41 pages, 2 figures, Lectures given at NATO Advanced Study Institute
on Quantum Fields and Quantum Space Time, Cargese, France, 22 July - 3 Augus
Integrable Classical and Quantum Gravity
In these lectures we report recent work on the exact quantization of dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space sigma-models coupled to gravity and a dilaton. Using methods developed in the context of flat space integrable systems, the Wheeler-DeWitt equations for these models can be reduced to a modified version of the Knizhnik-Zamolodchikov equations from conformal field theory, the insertions given by singularities in the spectral parameter plane. This basic result in principle permits the explicit construction of solutions, i.e. physical states of the quantized theory. In this way, we arrive at integrable models of quantum gravity with infinitely many self-interacting propagating degrees of freedom
Integrable Classical and Quantum Gravity
In these lectures we report recent work on the exact quantization of dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space sigma-models coupled to gravity and a dilaton. Using methods developed in the context of flat space integrable systems, the Wheeler-DeWitt equations for these models can be reduced to a modified version of the Knizhnik-Zamolodchikov equations from conformal field theory, the insertions given by singularities in the spectral parameter plane. This basic result in principle permits the explicit construction of solutions, i.e. physical states of the quantized theory. In this way, we arrive at integrable models of quantum gravity with infinitely many self-interacting propagating degrees of freedom
On quantum gravity coupled to a \s-model
This contribution is a review of the method of isomonodromic quantization of
dimensionally reduced gravity. Our approach is based on the complete separation
of variables in the isomonodromic sector of the model and the related
``two-time" Hamiltonian structure. This allows an exact quantization in the
spirit of the scheme developed in the framework of integrable systems. Possible
ways to identify a quantum state corresponding to the Kerr black hole are
discussed. In addition, we briefly describe the relation of this model with
Chern Simons theory.Comment: 9 pages, LaTeX style espcrc2, to appear in Proceedings of 29th
International Symposium Ahrenshoop, Buckow, 199
Poisson Realization and Quantization of the Geroch Group
The conserved nonlocal charges generating the Geroch group with respect to
the canonical Poisson structure of the Ernst equation are found. They are shown
to build a quadratic Poisson algebra, which suggests to identify the quantum
Geroch algebra with Yangian structures.Comment: 8 pages, LaTeX2
Canonical quantization of cylindrical gravitational waves with two polarizations
The canonical quantization of the essentially nonlinear midisuperspace model
describing cylindrically symmetric gravitational waves with two polarizations
is presented. A Fock space type representation is constructed. It is based on a
complete set of quantum observables. Physical expectation values may be
calculated in arbitrary excitations of the vacuum. Our approach provides a
non-linear generalization of the quantization of the collinearly polarized
Einstein-Rosen gravitational waves.Comment: 8 pages, LaTeX2