3,752 research outputs found
Mathematics of random growing interfaces
We establish a thermodynamic limit and Gaussian fluctuations for the height
and surface width of the random interface formed by the deposition of particles
on surfaces. The results hold for the standard ballistic deposition model as
well as the surface relaxation model in the off-lattice setting. The results
are proved with the aid of general limit theorems for stabilizing functionals
of marked Poisson point processes.Comment: 12 page
Interpreting doubly special relativity as a modified theory of measurement
In this article we develop a physical interpretation for the deformed
(doubly) special relativity theories (DSRs), based on a modification of the
theory of measurement in special relativity. We suggest that it is useful to
regard the DSRs as reflecting the manner in which quantum gravity effects
induce Planck-suppressed distortions in the measurement of the "true" energy
and momentum. This interpretation provides a framework for the DSRs that is
manifestly consistent, non-trivial, and in principle falsifiable. However, it
does so at the cost of demoting such theories from the level of "fundamental"
physics to the level of phenomenological models -- models that should in
principle be derivable from whatever theory of quantum gravity one ultimately
chooses to adopt.Comment: 18 pages, plain LaTeX2
Non-Standard Fermion Propagators from Conformal Field Theory
It is shown that Weyl spinors in 4D Minkowski space are composed of primary
fields of half-integer conformal weights. This yields representations of
fermionic 2-point functions in terms of correlators of primary fields with a
factorized transformation behavior under the Lorentz group. I employ this
observation to determine the general structure of the corresponding Lorentz
covariant correlators by methods similar to the methods employed in conformal
field theory to determine 2- and 3-point functions of primary fields. In
particular, the chiral symmetry breaking terms resemble fermionic 2-point
functions of 2D CFT up to a function of the product of momenta. The
construction also permits for the formulation of covariant meromorphy
constraints on spinors in 3+1 dimensions.Comment: 15 pages, Latex, LMU-TPW 94-1
Twistors, special relativity, conformal symmetry and minimal coupling - a review
An approach to special relativistic dynamics using the language of spinors
and twistors is presented. Exploiting the natural conformally invariant
symplectic structure of the twistor space, a model is constructed which
describes a relativistic massive, spinning and charged particle, minimally
coupled to an external electro-magnetic field. On the two-twistor phase space
the relativistic Hamiltonian dynamics is generated by a Poincare scalar
function obtained from the classical limit (appropriately defined by us) of the
second order, to an external electro-magnetic field minimally coupled, Dirac
operator. In the so defined relativistic classical limit there are no Grassman
variables. Besides, the arising equation that describes dynamics of the
relativistic spin differs significantly from the so called Thomas Bergman
Michel Telegdi equation.Comment: 39 pages, no figures, few erronous statements (not affecting anything
else in the papper) on page 23 delete
Can we see naked singularities?
We study singularities which can form in a spherically symmetric
gravitational collapse of a general matter field obeying weak energy condition.
We show that no energy can reach an outside observer from a null naked
singularity. That means they will not be a serious threat to the Cosmic
Censorship Conjecture (CCC). For the timelike naked singularities, where only
the central shell gets singular, the redshift is always finite and they can in
principle, carry energy to a faraway observer. Hence for proving or disproving
CCC the study of timelike naked singularities will be more important. Our
results are very general and are independent of initial data and the form of
the matter.Comment: 10 page
Decoherence of Macroscopic Closed Systems within Newtonian Quantum Gravity
A theory recently proposed by the author aims to explain decoherence and the
thermodynamical behaviour of closed systems within a conservative, unitary,
framework for quantum gravity by assuming that the operators tied to the
gravitational degrees of freedom are unobservable and equating physical entropy
with matter-gravity entanglement entropy. Here we obtain preliminary results on
the extent of decoherence this theory predicts. We treat first a static state
which, if one were to ignore quantum gravitational effects, would be a quantum
superposition of two spatially displaced states of a single classically well
describable ball of uniform mass density in empty space. Estimating the quantum
gravitational effects on this system within a simple Newtonian approximation,
we obtain formulae which predict e.g. that as long as the mass of the ball is
considerably larger than the Planck mass, such a would-be-coherent static
superposition will actually be decohered whenever the separation of the centres
of mass of the two ball-states excedes a small fraction (which decreases as the
mass of the ball increases) of the ball radius. We then obtain a formula for
the quantum gravitational correction to the would-be-pure density matrix of a
non-relativistic many-body Schroedinger wave function and argue that this
formula predicts decoherence between configurations which differ (at least) in
the "relocation" of a cluster of particles of Planck mass. We estimate the
entropy of some simple model closed systems, finding a tendency for it to
increase with "matter-clumping" suggestive of a link with existing
phenomenological discussions of cosmological entropy increase.Comment: 11 pages, plain TeX, no figures. Accepted for publication as a
"Letter to the Editor" in "Classical and Quantum Gravity
Prima Facie Questions in Quantum Gravity
The long history of the study of quantum gravity has thrown up a complex web
of ideas and approaches. The aim of this article is to unravel this web a
little by analysing some of the {\em prima facie\/} questions that can be asked
of almost any approach to quantum gravity and whose answers assist in
classifying the different schemes. Particular emphasis is placed on (i) the
role of background conceptual and technical structure; (ii) the role of
spacetime diffeomorphisms; and (iii) the problem of time.Comment: 20,IC/TP/0
The Stability of an Isotropic Cosmological Singularity in Higher-Order Gravity
We study the stability of the isotropic vacuum Friedmann universe in gravity
theories with higher-order curvature terms of the form
added to the Einstein-Hilbert Lagrangian of general relativity on approach to
an initial cosmological singularity. Earlier, we had shown that, when ,
a special isotropic vacuum solution exists which behaves like the
radiation-dominated Friedmann universe and is stable to anisotropic and small
inhomogeneous perturbations of scalar, vector and tensor type. This is
completely different to the situation that holds in general relativity, where
an isotropic initial cosmological singularity is unstable in vacuum and under a
wide range of non-vacuum conditions. We show that when , although a
special isotropic vacuum solution found by Clifton and Barrow always exists, it
is no longer stable when the initial singularity is approached. We find the
particular stability conditions under the influence of tensor, vector, and
scalar perturbations for general for both solution branches. On approach to
the initial singularity, the isotropic vacuum solution with scale factor
is found to be stable to tensor perturbations for and stable to vector perturbations for , but is
unstable as otherwise. The solution with scale factor
is not relevant to the case of an initial singularity for
and is unstable as for all for each type of perturbation.Comment: 25 page
The fields of uniformly accelerated charges in de Sitter spacetime
The scalar and electromagnetic fields of charges uniformly accelerated in de
Sitter spacetime are constructed. They represent the generalization of the Born
solutions describing fields of two particles with hyperbolic motion in flat
spacetime. In the limit Lambda -> 0, the Born solutions are retrieved. Since in
the de Sitter universe the infinities I^+- are spacelike, the radiative
properties of the fields depend on the way in which a given point of I^+- is
approached. The fields must involve both retarded and advanced effects: Purely
retarded fields do not satisfy the constraints at the past infinity I^-.Comment: 5 pages, 3 figures, RevTeX; Slightly expanded version of the paper
published in Physical Review Letters. (The published version can be generated
from the same TeX source.); problem with the postscript fixe
The Googly Amplitudes in Gauge Theory
The googly amplitudes in gauge theory are computed by using the off shell MHV
vertices with the newly proposed rules of Cachazo, Svrcek and Witten. The
result is in agreement with the previously well-known results. In particular we
also obtain a simple result for the all negative but one positive helicity
amplitude when one of the external line is off shell.Comment: Latex file, 16 pages, 7 figures. Figures may bot display correctly in
ps file. Pls use pdf file instea
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