125 research outputs found
Statistical description of the black hole degeneracy spectrum
We use mathematical methods based on generating functions to study the
statistical properties of the black hole degeneracy spectrum in loop quantum
gravity. In particular we will study the persistence of the observed effective
quantization of the entropy as a function of the horizon area. We will show
that this quantization disappears as the area increases despite the existence
of black hole configurations with a large degeneracy. The methods that we
describe here can be adapted to the study of the statistical properties of the
black hole degeneracy spectrum for all the existing proposals to define black
hole entropy in loop quantum gravity.Comment: 41 pages, 12 figure
Introduction to Quantum Mechanics
The purpose of this contribution is to give a very brief introduction to
Quantum Mechanics for an audience of mathematicians. I will follow Segal's
approach to Quantum Mechanics paying special attention to algebraic issues. The
usual representation of Quantum Mechanics on Hilbert spaces is also discussed.Comment: To appear in the AIP Conference Proceedings of the XVI International
Fall Workshop on Geometry and Physics, Lisbon - Portugal, 5-8 September 2007.
11 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
Quantum isolated horizons and black hole entropy
We give a short introduction to the approaches currently used to describe
black holes in loop quantum gravity. We will concentrate on the classical
issues related to the modeling of black holes as isolated horizons, give a
short discussion of their canonical quantization by using loop quantum gravity
techniques, and a description of the combinatorial methods necessary to solve
the counting problems involved in the computation of the entropy.Comment: 28 pages in A4 format. Contribution to the Proceedings of the 3rd
Quantum Geometry and Quantum Gravity School in Zakopane (2011
The time-dependent quantum harmonic oscillator revisited: Applications to Quantum Field Theory
In this article, we formulate the study of the unitary time evolution of
systems consisting of an infinite number of uncoupled time-dependent harmonic
oscillators in mathematically rigorous terms. We base this analysis on the
theory of a single one-dimensional time-dependent oscillator, for which we
first summarize some basic results concerning the unitary implementability of
the dynamics. This is done by employing techniques different from those used so
far to derive the Feynman propagator. In particular, we calculate the
transition amplitudes for the usual harmonic oscillator eigenstates and define
suitable semiclassical states for some physically relevant models. We then
explore the possible extension of this study to infinite dimensional dynamical
systems. Specifically, we construct Schroedinger functional representations in
terms of appropriate probability spaces, analyze the unitarity of the time
evolution, and probe the existence of semiclassical states for a wide range of
physical systems, particularly, the well-known Minkowskian free scalar fields
and Gowdy cosmological models.Comment: 31 pages, 3 figures. Accepted for publication in Annals of Physic
Proof of the equivalence of the symplectic forms derived from the canonical and the covariant phase space formalisms
We prove that, for any theory defined over a space-time with boundary, the
symplectic form derived in the covariant phase space is equivalent to the one
derived from the canonical formalism.Comment: Accepted in PR
Probing Quantized Einstein-Rosen Waves with Massless Scalar Matter
The purpose of this paper is to discuss in detail the use of scalar matter
coupled to linearly polarized Einstein-Rosen waves as a probe to study quantum
gravity in the restricted setting provided by this symmetry reduction of
general relativity. We will obtain the relevant Hamiltonian and quantize it
with the techniques already used for the purely gravitational case. Finally we
will discuss the use of particle-like modes of the quantized fields to
operationally explore some of the features of quantum gravity within this
framework. Specifically we will study two-point functions, the Newton-Wigner
propagator, and radial wave functions for one-particle states.Comment: Accepted for publication in Physical Review
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