387 research outputs found
Loop Quantization of Maxwell Theory and Electric Charge Quantization
We consider the loop quantization of Maxwell theory. A quantization of this
type leads to a quantum theory in which the fundamental excitations are
loop-like rather than particle-like. Each such loop plays the role of a
quantized Faraday's line of electric flux. We find that the quantization
depends on an arbitrary choice of a parameter e that carries the dimension of
electric charge. For each value of e an electric charge that can be contained
inside a bounded spatial region is automatically quantized in units of
hbar/4*pi*e. The requirement of consistency with the quantization of electric
charge observed in our Universe fixes a value of the, so far arbitrary,
parameter e of the theory. Finally, we compare the ambiguity in the choice of
parameter e with the beta-ambiguity that, as pointed by Immirzi, arises in the
loop quantization of general relativity, and comment on a possible way this
ambiguity can be fixed.Comment: 7 pages, Revtex, no figures, typos corrected and one reference adde
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-
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.
The physical hamiltonian in nonperturbative quantum gravity
A quantum hamiltonian which evolves the gravitational field according to time
as measured by constant surfaces of a scalar field is defined through a
regularization procedure based on the loop representation, and is shown to be
finite and diffeomorphism invariant. The problem of constructing this
hamiltonian is reduced to a combinatorial and algebraic problem which involves
the rearrangements of lines through the vertices of arbitrary graphs. This
procedure also provides a construction of the hamiltonian constraint as a
finite operator on the space of diffeomorphism invariant states as well as a
construction of the operator corresponding to the spatial volume of the
universe.Comment: Latex, 11 pages, no figures, CGPG/93/
A local Hamiltonian for spherically symmetric gravity coupled to a scalar field
We present a gauge fixing of gravity coupled to a scalar field in spherical
symmetry such that the Hamiltonian is an integral over space of a local
density. Such a formulation had proved elusive over the years. As in any gauge
fixing, it works for a restricted set of initial data. We argue that the set
could be large enough to attempt a quantization the could include the important
case of an evaporating black hole.Comment: 4 pages, no figures, RevTex, final published versio
Canonical quantum gravity in the Vassiliev invariants arena: I. Kinematical structure
We generalize the idea of Vassiliev invariants to the spin network context,
with the aim of using these invariants as a kinematical arena for a canonical
quantization of gravity. This paper presents a detailed construction of these
invariants (both ambient and regular isotopic) requiring a significant
elaboration based on the use of Chern-Simons perturbation theory which extends
the work of Kauffman, Martin and Witten to four-valent networks. We show that
this space of knot invariants has the crucial property -from the point of view
of the quantization of gravity- of being loop differentiable in the sense of
distributions. This allows the definition of diffeomorphism and Hamiltonian
constraints. We show that the invariants are annihilated by the diffeomorphism
constraint. In a companion paper we elaborate on the definition of a
Hamiltonian constraint, discuss the constraint algebra, and show that the
construction leads to a consistent theory of canonical quantum gravity.Comment: 21 Pages, RevTex, many figures included with psfi
Loop Representations
The loop representation plays an important role in canonical quantum gravity
because loop variables allow a natural treatment of the constraints. In these
lectures we give an elementary introduction to (i) the relevant history of
loops in knot theory and gauge theory, (ii) the loop representation of Maxwell
theory, and (iii) the loop representation of canonical quantum gravity. (Based
on lectures given at the 117. Heraeus Seminar, Bad Honnef, Sept. 1993)Comment: 38 pages, MPI-Ph/93-9
Testing kappa-Poincare' with neutral kaons
In recent work on experimental tests of quantum-gravity-motivated
phenomenological models, a significant role has been played by the so-called
``'' deformations of Poincar\'e symmetries. Sensitivity to values of
the relevant deformation length as small as has
been achieved in recent analyses comparing the structure of -Poincar\'e
symmetries with data on the gamma rays we detect from distant astrophysical
sources. We investigate violations of CPT symmetry which may be associated with
-Poincar\'e in the physics of the neutral-kaon system. A simple
estimate indicates that experiments on the neutral kaons may actually be more
-sensitive than corresponding astrophysical experiments, and may
already allow to probe values of of order the Planck length.Comment: 9 pages, LaTe
Spin Networks and Quantum Gravity
We introduce a new basis on the state space of non-perturbative quantum
gravity. The states of this basis are linearly independent, are well defined in
both the loop representation and the connection representation, and are labeled
by a generalization of Penrose's spin netoworks. The new basis fully reduces
the spinor identities (SU(2) Mandelstam identities) and simplifies calculations
in non-perturbative quantum gravity. In particular, it allows a simple
expression for the exact solutions of the Hamiltonian constraint
(Wheeler-DeWitt equation) that have been discovered in the loop representation.
Since the states in this basis diagnolize operators that represent the three
geometry of space, such as the area and volumes of arbitrary surfaces and
regions, these states provide a discrete picture of quantum geometry at the
Planck scale.Comment: 42 page
Multiple-event probability in general-relativistic quantum mechanics: a discrete model
We introduce a simple quantum mechanical model in which time and space are
discrete and periodic. These features avoid the complications related to
continuous-spectrum operators and infinite-norm states. The model provides a
tool for discussing the probabilistic interpretation of generally-covariant
quantum systems, without the confusion generated by spurious infinities. We use
the model to illustrate the formalism of general-relativistic quantum
mechanics, and to test the definition of multiple-event probability introduced
in a companion paper. We consider a version of the model with unitary
time-evolution and a version without unitary time-evolutio
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