379 research outputs found
Classical and quantum general relativity: a new paradigm
We argue that recent developments in discretizations of classical and quantum
gravity imply a new paradigm for doing research in these areas. The paradigm
consists in discretizing the theory in such a way that the resulting discrete
theory has no constraints. This solves many of the hard conceptual problems of
quantum gravity. It also appears as a useful tool in some numerical simulations
of interest in classical relativity. We outline some of the salient aspects and
results of this new framework.Comment: 8 pages, one figure, fifth prize of the Gravity Research Foundation
2005 essay competitio
Fundamental decoherence from relational time in discrete quantum gravity: Galilean covariance
We have recently argued that if one introduces a relational time in quantum
mechanics and quantum gravity, the resulting quantum theory is such that pure
states evolve into mixed states. The rate at which states decohere depends on
the energy of the states. There is therefore the question of how this can be
reconciled with Galilean invariance. More generally, since the relational
description is based on objects that are not Dirac observables, the issue of
covariance is of importance in the formalism as a whole. In this note we work
out an explicit example of a totally constrained, generally covariant system of
non-relativistic particles that shows that the formula for the relational
conditional probability is a Galilean scalar and therefore the decoherence rate
is invariant.Comment: 10 pages, RevTe
Lattice knot theory and quantum gravity in the loop representation
We present an implementation of the loop representation of quantum gravity on
a square lattice. Instead of starting from a classical lattice theory,
quantizing and introducing loops, we proceed backwards, setting up constraints
in the lattice loop representation and showing that they have appropriate
(singular) continuum limits and algebras. The diffeomorphism constraint
reproduces the classical algebra in the continuum and has as solutions lattice
analogues of usual knot invariants. We discuss some of the invariants stemming
from Chern--Simons theory in the lattice context, including the issue of
framing. We also present a regularization of the Hamiltonian constraint. We
show that two knot invariants from Chern--Simons theory are annihilated by the
Hamiltonian constraint through the use of their skein relations, including
intersections. We also discuss the issue of intersections with kinks. This
paper is the first step towards setting up the loop representation in a
rigorous, computable setting.Comment: 23 pages, RevTeX, 14 figures included with psfi
A Geometric Representation for the Proca Model
The Proca model is quantized in an open-path dependent representation that
generalizes the Loop Representation of gauge theories. The starting point is a
gauge invariant Lagrangian that reduces to the Proca Lagrangian when certain
gauge is selected.Comment: 10 pages, Late
No black hole information puzzle in a relational universe
The introduction of a relational time in quantum gravity naturally implies
that pure quantum states evolve into mixed quantum states. We show, using a
recently proposed concrete implementation, that the rate at which pure states
naturally evolve into mixed ones is faster than that due to collapsing into a
black hole that later evaporates. This is rather remarkable since the
fundamental mechanism for decoherence is usually very weak. Therefore the
``black hole information puzzle'' is rendered de-facto unobservable.Comment: 4 pages, no figures, revte
Conditional probabilities with Dirac observables and the problem of time in quantum gravity
We combine the "evolving constants" approach to the construction of
observables in canonical quantum gravity with the Page--Wootters formulation of
quantum mechanics with a relational time for generally covariant systems. This
overcomes the objections levied by Kucha\v{r} against the latter formalism. The
construction is formulated entirely in terms of Dirac observables, avoiding in
all cases the physical observation of quantities that do not belong in the
physical Hilbert space. We work out explicitly the example of the parameterized
particle, including the calculation of the propagator. The resulting theory
also predicts a fundamental mechanism of decoherence.Comment: 4 pages, no figures, RevTe
The Montevideo interpretation of quantum mechanics: frequently asked questions
In a series of recent papers we have introduced a new interpretation of
quantum mechanics, which for brevity we will call the Montevideo
interpretation. In it, the quantum to classical transition is achieved via a
phenomenon called "undecidability" which stems from environmental decoherence
supplemented with a fundamental mechanism of loss of coherence due to gravity.
Due to the fact that the interpretation grew from several results that are
dispersed in the literature, we put together this straightforward-to-read
article addressing some of the main points that may confuse readers.Comment: 11 pages, no figures, to appear in J. Phys. Conf. Series, proceedings
of the DICE 2008 Castiglioncello meetin
Loop Variables for compact two-dimensional quantum electrodynamics
Variables parametrized by closed and open curves are defined to reformulate
compact U(1) Quantum Electrodynamics in the circle with a massless fermion
field. It is found that the gauge invariant nature of these variables
accommodates into a regularization scheme for the Hamiltonian and current
operators that is specially well suited for the study of the compact case. The
zero mode energy spectrum, the value of the axial anomaly and the anomalous
commutators this model presents are hence determined in a manifestly gauge
invariant manner. Contrary to the non compact case, the zero mode spectrum is
not equally spaced and consequently the theory does not lead to the spectrum of
a free scalar boson. All the states are invariant under large gauge
transformations. In particular, that is the case for the vacuum, and
consequently the -dependence does not appear.Comment: 24 pages, 1 figure, to be published in Phys. Rev.
Covariant Duality Symmetric Actions
A manifestly Lorentz and diffeomorphism invariant form for the abelian gauge
field action with local duality symmetry of Schwarz and Sen is given. Some of
the underlying symmetries of the covariant action are further considered. The
Noether conserved charge under continuous local duality rotations is found. The
covariant couplings with gravity and the axidilaton field are discussed.Comment: 9 pages, revtex, no figures; (To appear in Physical Review D
A physical distinction between a covariant and non covariant reduction process in relativistic quantum theories
Causality imposes strong restrictions on the type of operators that may be
observables in relativistic quantum theories. In fact, causal violations arise
when computing conditional probabilities for certain partial causally connected
measurements using the standard non covariant procedure. Here we introduce
another way of computing conditional probabilities, based on an intrinsic
covariant relational order of the events, which differs from the standard one
when these type of measurements are included. This alternative procedure is
compatible with a wider and very natural class of operators without breaking
causality. If some of these measurements could be implemented in practice as
predicted by our formalism, the non covariant, conventional approach should be
abandoned. Furthermore, the description we promote here would imply a new
physical effect where interference terms are suppressed as a consequence of the
covariant order in the measurement process.Comment: 7 pages, latex file, 1 ps figure. Major presentation changes. To
appear in New Journal of Physic
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