653 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
Canonical quantum gravity in the Vassiliev invariants arena: II. Constraints, habitats and consistency of the constraint algebra
In a companion paper we introduced a kinematical arena for the discussion of
the constraints of canonical quantum gravity in the spin network representation
based on Vassiliev invariants. In this paper we introduce the Hamiltonian
constraint, extend the space of states to non-diffeomorphism invariant
``habitats'' and check that the off-shell quantum constraint commutator algebra
reproduces the classical Poisson algebra of constraints of general relativity
without anomalies. One can therefore consider the resulting set of constraints
and space of states as a consistent theory of canonical quantum gravity.Comment: 20 Pages, RevTex, many figures included with psfi
Discrete quantum gravity: a mechanism for selecting the value of fundamental constants
Smolin has put forward the proposal that the universe fine tunes the values
of its physical constants through a Darwinian selection process. Every time a
black hole forms, a new universe is developed inside it that has different
values for its physical constants from the ones in its progenitor. The most
likely universe is the one which maximizes the number of black holes. Here we
present a concrete quantum gravity calculation based on a recently proposed
consistent discretization of the Einstein equations that shows that fundamental
physical constants change in a random fashion when tunneling through a
singularity.Comment: 5 pages, RevTex, 4 figures, honorable mention in the 2003 Gravity
Research Foundation Essays, to appear in Int. J. Mod. Phys.
Classical Loop Actions of Gauge Theories
Since the first attempts to quantize Gauge Theories and Gravity in the loop
representation, the problem of the determination of the corresponding classical
actions has been raised. Here we propose a general procedure to determine these
actions and we explicitly apply it in the case of electromagnetism. Going to
the lattice we show that the electromagnetic action in terms of loops is
equivalent to the Wilson action, allowing to do Montecarlo calculations in a
gauge invariant way. In the continuum these actions need to be regularized and
they are the natural candidates to describe the theory in a ``confining
phase''.Comment: LaTeX 14 page
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
Finite, diffeomorphism invariant observables in quantum gravity
Two sets of spatially diffeomorphism invariant operators are constructed in
the loop representation formulation of quantum gravity. This is done by
coupling general relativity to an anti- symmetric tensor gauge field and using
that field to pick out sets of surfaces, with boundaries, in the spatial three
manifold. The two sets of observables then measure the areas of these surfaces
and the Wilson loops for the self-dual connection around their boundaries. The
operators that represent these observables are finite and background
independent when constructed through a proper regularization procedure.
Furthermore, the spectra of the area operators are discrete so that the
possible values that one can obtain by a measurement of the area of a physical
surface in quantum gravity are valued in a discrete set that includes integral
multiples of half the Planck area. These results make possible the construction
of a correspondence between any three geometry whose curvature is small in
Planck units and a diffeomorphism invariant state of the gravitational and
matter fields. This correspondence relies on the approximation of the classical
geometry by a piecewise flat Regge manifold, which is then put in
correspondence with a diffeomorphism invariant state of the gravity-matter
system in which the matter fields specify the faces of the triangulation and
the gravitational field is in an eigenstate of the operators that measure their
areas.Comment: Latex, no figures, 30 pages, SU-GP-93/1-
Uniform discretizations: a new approach for the quantization of totally constrained systems
We discuss in detail the uniform discretization approach to the quantization
of totally constrained theories. This approach allows to construct the
continuum theory of interest as a well defined, controlled, limit of well
behaved discrete theories. We work out several finite dimensional examples that
exhibit behaviors expected to be of importance in the quantization of gravity.
We also work out the case of BF theory. At the time of quantization, one can
take two points of view. The technique can be used to define, upon taking the
continuum limit, the space of physical states of the continuum constrained
theory of interest. In particular we show in models that it agrees with the
group averaging procedure when the latter exists. The technique can also be
used to compute, at the discrete level, conditional probabilities and the
introduction of a relational time. Upon taking the continuum limit one can show
that one reproduces results obtained by the use of evolving constants, and
therefore recover all physical predictions of the continuum theory. This second
point of view can also be used as a paradigm to deal with cases where the
continuum limit does not exist. There one would have discrete theories that at
least at certain scales reproduce the semiclassical properties of the theory of
interest. In this way the approach can be viewed as a generalization of the
Dirac quantization procedure that can handle situations where the latter fails.Comment: 17 pages, Revtex, no figures, published versio
The Extended Loop Representation of Quantum Gravity
A new representation of Quantum Gravity is developed. This formulation is
based on an extension of the group of loops. The enlarged group, that we call
the Extended Loop Group, behaves locally as an infinite dimensional Lie group.
Quantum Gravity can be realized on the state space of extended loop dependent
wavefunctions. The extended representation generalizes the loop representation
and contains this representation as a particular case. The resulting
diffeomorphism and hamiltonian constraints take a very simple form and allow to
apply functional methods and simplify the loop calculus. In particular we show
that the constraints are linear in the momenta. The nondegenerate solutions
known in the loop representation are also solutions of the constraints in the
new representation. The practical calculation advantages allows to find a new
solution to the Wheeler-DeWitt equation. Moreover, the extended representation
puts in a precise framework some of the regularization problems of the loop
representation. We show that the solutions are generalized knot invariants,
smooth in the extended variables, and any framing is unnecessary.Comment: 27 pages, report IFFC/94-1
Relativistic quantum measurement
Does the measurement of a quantum system necessarily break Lorentz
invariance? We present a simple model of a detector that measures the spacetime
localization of a relativistic particle in a Lorentz invariant manner. The
detector does not select a preferred Lorentz frame as a Newton-Wigner
measurement would do. The result indicates that there exists a Lorentz
invariant notion of quantum measurement and sheds light on the issue of the
localization of a relativistic particle. The framework considered is that of
single-particle mechanics as opposed to field theory. The result may be taken
as support for the interpretation postulate of the spacetime-states formulation
of single-particle quantum theory.Comment: 9 pages, no figures: Revision: references adde
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