18,920 research outputs found
The gravitational S-matrix: Erice lectures
These lectures discuss an S-matrix approach to quantum gravity, and its
relation to more local spacetime approaches. Prominent among the problems of
quantum gravity are those of unitarity and observables. In a unitary theory
with solutions approximating Minkowski space, the S-matrix (or, in four
dimensions, related inclusive probabilities) should be sharply formulated and
physical. Features of its perturbative description are reviewed. A successful
quantum gravity theory should in particular address the questions posed by the
ultrahigh-energy regime. Some control can be gained in this regime by varying
the impact parameter as well as the collision energy. However, with decreasing
impact parameter gravity becomes strong, first eikonalizing, and then entering
the regime where in the classical approximation black holes form. Here one
confronts what may be the most profound problem of quantum gravity, that of
providing unitary amplitudes, as seen through the information problem of black
hole evaporation. Existing approaches to quantum gravity leave a number of
unanswered questions in this regime; there are strong indications that new
principles and mechanisms are needed, and in particular there is a good case
that usual notions of locality are inaccurate. One approach to these questions
is investigation of the approximate local dynamics of spacetime, its
observables, and its limitations; another is to directly explore properties of
the gravitational S-matrix, such as analyticity, crossing, and others implied
by gravitational physics.Comment: 44 pages, 15 figures; with exercises. Lectures presented at the 48th
Course of the Erice International School of Subnuclear Physics, "What is
known and unexpected at LHC," Aug./Sept. 2010. v2: repaired referenc
Emergent Spacetime
We summarize the arguments that space and time are likely to be emergent
notions; i.e. they are not present in the fundamental formulation of the
theory, but appear as approximate macroscopic concepts. Along the way we
briefly review certain topics. These include ambiguities in the geometry and
the topology of space which arise from dualities, questions associated with
locality, various known examples of emergent space, and the puzzles and the
prospects of emergent time.Comment: Rapporteur talk at the 23rd Solvay Conference in Physics, December,
2005. 24 page
FIFO anomaly is unbounded
Virtual memory of computers is usually implemented by demand paging. For some
page replacement algorithms the number of page faults may increase as the
number of page frames increases. Belady, Nelson and Shedler constructed
reference strings for which page replacement algorithm FIFO produces near twice
more page faults in a larger memory than in a smaller one. They formulated the
conjecture that 2 is a general bound. We prove that this ratio can be
arbitrarily large
The role of the Beltrami parametrization of complex structures in 2-d Free Conformal Field Theory
This talk gives a review on how complex geometry and a Lagrangian formulation
of 2-d conformal field theory are deeply related. In particular, how the use of
the Beltrami parametrization of complex structures on a compact Riemann surface
fits perfectly with the celebrated locality principle of field theory, the
latter requiring the use infinite dimensional spaces. It also allows a direct
application of the local index theorem for families of elliptic operators due
to J.-M. Bismut, H. Gillet and C. Soul\'{e}. The link between determinant line
bundles equipped with the Quillen\'s metric and the so-called holomorphic
factorization property will be addressed in the case of free spin b-c
systems or more generally of free fields with values sections of a holomorphic
vector bundles over a compact Riemann surface.Comment: Actes du Colloque "Complex Geometry '98
Is string theory a theory of quantum gravity?
Some problems in finding a complete quantum theory incorporating gravity are
discussed. One is that of giving a consistent unitary description of
high-energy scattering. Another is that of giving a consistent quantum
description of cosmology, with appropriate observables. While string theory
addresses some problems of quantum gravity, its ability to resolve these
remains unclear. Answers may require new mechanisms and constructs, whether
within string theory, or in another framework.Comment: Invited contribution for "Forty Years of String Theory: Reflecting on
the Foundations," a special issue of Found. Phys., ed. by G 't Hooft, E.
Verlinde, D. Dieks, S. de Haro. 32 pages, 5 figs., harvmac. v2: final version
to appear in journal (small revisions
Learning to Read by Spelling: Towards Unsupervised Text Recognition
This work presents a method for visual text recognition without using any
paired supervisory data. We formulate the text recognition task as one of
aligning the conditional distribution of strings predicted from given text
images, with lexically valid strings sampled from target corpora. This enables
fully automated, and unsupervised learning from just line-level text-images,
and unpaired text-string samples, obviating the need for large aligned
datasets. We present detailed analysis for various aspects of the proposed
method, namely - (1) impact of the length of training sequences on convergence,
(2) relation between character frequencies and the order in which they are
learnt, (3) generalisation ability of our recognition network to inputs of
arbitrary lengths, and (4) impact of varying the text corpus on recognition
accuracy. Finally, we demonstrate excellent text recognition accuracy on both
synthetically generated text images, and scanned images of real printed books,
using no labelled training examples
The information paradox and the locality bound
Hawking's argument for information loss in black hole evaporation rests on
the assumption of independent Hilbert spaces for the interior and exterior of a
black hole. We argue that such independence cannot be established without
incorporating strong gravitational effects that undermine locality and
invalidate the use of quantum field theory in a semiclassical background
geometry. These considerations should also play a role in a deeper
understanding of horizon complementarity.Comment: 21 pages, harvmac; v2-3. minor corrections, references adde
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