11 research outputs found
Weakly Isolated Horizons: decomposition and canonical formulations in self-dual variables
The notion of Isolated Horizons has played an important role in gravitational
physics, being useful from the characterization of the endpoint of black hole
mergers to (quantum) black hole entropy. In particular, the definition of {\it
weakly} isolated horizons (WIHs) as quasilocal generalizations of event
horizons is purely geometrical, and is independent of the variables used in
describing the gravitational field. Here we consider a canonical decomposition
of general relativity in terms of connection and vierbein variables starting
from a first order action. Within this approach, the information about the
existence of a (weakly) isolated horizon is obtained through a set of boundary
conditions on an internal boundary of the spacetime region under consideration.
We employ, for the self-dual action, a generalization of the Dirac algorithm
for regions with boundary. While the formalism for treating gauge theories with
boundaries is unambiguous, the choice of dynamical variables on the boundary is
not. We explore this freedom and consider different canonical formulations for
non-rotating black holes as defined by WIHs. We show that both the notion of
horizon degrees of freedom and energy associated to the horizon is not unique,
even when the descriptions might be self-consistent. This represents a
generalization of previous work on isolated horizons both in the exploration of
this freedom and in the type of horizons considered. We comment on previous
results found in the literature.Comment: 33 pages, no figures. Typos correcte
Hamiltonian and physical Hilbert space in polymer quantum mechanics
In this paper, a version of polymer quantum mechanics, which is inspired by
loop quantum gravity, is considered and shown to be equivalent, in a precise
sense, to the standard, experimentally tested, Schroedinger quantum mechanics.
The kinematical cornerstone of our framework is the so called polymer
representation of the Heisenberg-Weyl (H-W) algebra, which is the starting
point of the construction. The dynamics is constructed as a continuum limit of
effective theories characterized by a scale, and requires a renormalization of
the inner product. The result is a physical Hilbert space in which the
continuum Hamiltonian can be represented and that is unitarily equivalent to
the Schroedinger representation of quantum mechanics. As a concrete
implementation of our formalism, the simple harmonic oscillator is fully
developed.Comment: 19 pages, 2 figures. Comments and references added. Version to be
published in CQ
On Covariant and Canonical Hamiltonian Formalisms for Gauge Theories
The Hamiltonian description of classical gauge theories is a very well studied subject. The two best known approaches, namely the covariant and canonical Hamiltonian formalisms, have received a lot of attention in the literature. However, a full understanding of the relation between them is not available, especially when the gauge theories are defined over regions with boundaries. Here, we consider this issue, by first making it precise what we mean by equivalence between the two formalisms. Then, we explore several first-order gauge theories and assess whether their corresponding descriptions satisfy the notion of equivalence. We shall show that, even when in several cases the two formalisms are indeed equivalent, there are counterexamples that signal that this is not always the case. Thus, non-equivalence is a generic feature of gauge field theories. These results call for a deeper understanding of the subject