52 research outputs found
Learning about Quantum Gravity with a Couple of Nodes
Loop Quantum Gravity provides a natural truncation of the infinite degrees of
freedom of gravity, obtained by studying the theory on a given finite graph. We
review this procedure and we present the construction of the canonical theory
on a simple graph, formed by only two nodes. We review the U(N) framework,
which provides a powerful tool for the canonical study of this model, and a
formulation of the system based on spinors. We consider also the covariant
theory, which permits to derive the model from a more complex formulation,
paying special attention to the cosmological interpretation of the theory
U(N) and holomorphic methods for LQG and Spin Foams
The U(N) framework and the spinor representation for loop quantum gravity are
two new points of view that can help us deal with the most fundamental problems
of the theory. Here, we review the detailed construction of the U(N) framework
explaining how one can endow the Hilbert space of N-leg intertwiners with a
Fock structure. We then give a description of the classical phase space
corresponding to this system in terms of the spinors, and we will study its
quantization using holomorphic techniques. We take special care in constructing
the usual holonomy operators of LQG in terms of spinors, and in the description
of the Hilbert space of LQG with the different polarization given by these
spinors.Comment: 16 pages. Proceedings for the 3rd Quantum Geometry and Quantum
Gravity School in Zakopane (2011
U(N) tools for Loop Quantum Gravity: The Return of the Spinor
We explore the classical setting for the U(N) framework for SU(2)
intertwiners for loop quantum gravity (LQG) and describe the corresponding
phase space in terms of spinors with appropriate constraints. We show how its
quantization leads back to the standard Hilbert space of intertwiner states
defined as holomorphic functionals. We then explain how to glue these
intertwiners states in order to construct spin network states as wave-functions
on the spinor phase space. In particular, we translate the usual loop gravity
holonomy observables to our classical framework. Finally, we propose how to
derive our phase space structure from an action principle which induces
non-trivial dynamics for the spin network states. We conclude by applying
explicitly our framework to states living on the simple 2-vertex graph and
discuss the properties of the resulting Hamiltonian.Comment: 23 page
Classical and quantum behavior of dynamical systems defined by functions of solvable Hamiltonians
We discuss the classical and quantum mechanical evolution of systems
described by a Hamiltonian that is a function of a solvable one, both
classically and quantum mechanically. The case in which the solvable
Hamiltonian corresponds to the harmonic oscillator is emphasized. We show that,
in spite of the similarities at the classical level, the quantum evolution is
very different. In particular, this difference is important in constructing
coherent states, which is impossible in most cases. The class of Hamiltonians
we consider is interesting due to its pedagogical value and its applicability
to some open research problems in quantum optics and quantum gravity.Comment: Accepted for publication in American Journal of Physic
Cuantización de ondas de Einstein-Rosen acopladas con materia
Tesis doctoral inédita. Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica. Fecha de lectura: 22-06-0
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