2,903 research outputs found
Duality theory and propagation rules for higher order nets
AbstractHigher order nets and sequences are used in quasi-Monte Carlo rules for the approximation of high dimensional integrals over the unit cube. Hence one wants to have higher order nets and sequences of high quality.In this paper we introduce a duality theory for higher order nets whose construction is not necessarily based on linear algebra over finite fields. We use this duality theory to prove propagation rules for such nets. This way we can obtain new higher order nets (sometimes with improved quality) from existing ones. We also extend our approach to the construction of higher order sequences
Recent advances in higher order quasi-Monte Carlo methods
In this article we review some of recent results on higher order quasi-Monte
Carlo (HoQMC) methods. After a seminal work by Dick (2007, 2008) who originally
introduced the concept of HoQMC, there have been significant theoretical
progresses on HoQMC in terms of discrepancy as well as multivariate numerical
integration. Moreover, several successful and promising applications of HoQMC
to partial differential equations with random coefficients and Bayesian
estimation/inversion problems have been reported recently. In this article we
start with standard quasi-Monte Carlo methods based on digital nets and
sequences in the sense of Niederreiter, and then move onto their higher order
version due to Dick. The Walsh analysis of smooth functions plays a crucial
role in developing the theory of HoQMC, and the aim of this article is to
provide a unified picture on how the Walsh analysis enables recent developments
of HoQMC both for discrepancy and numerical integration
Neural network parametrization of spectral functions from hadronic tau decays and determination of QCD vacuum condensates
The spectral function is determined from ALEPH and OPAL data
on hadronic tau decays using a neural network parametrization trained to retain
the full experimental information on errors, their correlations and chiral sum
rules: the DMO sum rule, the first and second Weinberg sum rules and the
electromagnetic mass splitting of the pion sum rule. Nonperturbative QCD vacuum
condensates can then be determined from finite energy sum rules. Our method
minimizes all sources of theoretical uncertainty and bias producing an estimate
of the condensates which is independent of the specific finite energy sum rule
used. The results for the central values of the condensates and are
both negative.Comment: 29 pages, 18 ps figure
The Pivotal Role of Causality in Local Quantum Physics
In this article an attempt is made to present very recent conceptual and
computational developments in QFT as new manifestations of old and well
establihed physical principles. The vehicle for converting the
quantum-algebraic aspects of local quantum physics into more classical
geometric structures is the modular theory of Tomita. As the above named
laureate to whom I have dedicated has shown together with his collaborator for
the first time in sufficient generality, its use in physics goes through
Einstein causality. This line of research recently gained momentum when it was
realized that it is not only of structural and conceptual innovative power (see
section 4), but also promises to be a new computational road into
nonperturbative QFT (section 5) which, picturesquely speaking, enters the
subject on the extreme opposite (noncommutative) side.Comment: This is a updated version which has been submitted to Journal of
Physics A, tcilatex 62 pages. Adress: Institut fuer Theoretische Physik
FU-Berlin, Arnimallee 14, 14195 Berlin presently CBPF, Rua Dr. Xavier Sigaud
150, 22290-180 Rio de Janeiro, Brazi
Braided Structure in 4-dimensional conformal Quantum Field Theory
Higher dimensional conformal QFT possesses an interesting braided structure
which, different from the d=1+1 models, is restricted to the timelike region
and therefore easily escapes euclidean action methods. It lies behind the
spectrum of anomalous dimensions which may be viewed as a kind of substitute
for a missing particle interpretation in the presence of interactions.Comment: Dedicated to Gerhard Mack and Robert Schrader on the occasion of
their 60th birthday, submitted to Phys. Lett. B, 10 pages, improvements of
the formulation, shortening of the text, addition of a formula, removal of
typo
Anomalous Scale Dimensions from Timelike Braiding
Using the previously gained insight about the particle/field relation in
conformal quantum field theories which required interactions to be related to
the existence of particle-like states associated with fields of anomalous
scaling dimensions, we set out to construct a classification theory for the
spectra of anomalous dimensions. Starting from the old observations on
conformal superselection sectors related to the anomalous dimensions via the
phases which appear in the spectral decomposition of the center of the
conformal covering group we explore the possibility
of a timelike braiding structure consistent with the timelike ordering which
refines and explains the central decomposition. We regard this as a preparatory
step in a new construction attempt of interacting conformal quantum field
theories in D=4 spacetime dimensions. Other ideas of constructions based on the
- or the perturbative SYM approach in their relation to the
present idea are briefly mentioned.Comment: completely revised, updated and shortened replacement, 24 pages
tcilatex, 3 latexcad figure
Facts and Fictions about Anti deSitter Spacetimes with Local Qantum Matter
It is natural to analyse the AdS-CQFT correspondence in the
context of the conformal- compactification and covering formalism. In this way
one obtains additional inside about Rehren's rigorous algebraic holography in
connection with the degree of freedom issue which in turn allows to illustrates
the subtle but important differences beween the original string theory-based
Maldacena conjecture and Rehren's theorem in the setting of an intrinsic
field-coordinatization-free formulation of algebraic QFT. I also discuss
another more generic type of holography related to light fronts which seems to
be closer to 't Hooft's original ideas on holography. This in turn is naturally
connected with the generic concept of ``Localization Entropy'', a quantum
pre-form of Bekenstein's classical black-hole surface entropy.Comment: this final version is identical to the one which appeared in Commun.
Math. Phys. 219, (2001) 57-76, an issue of CMP dedicated to the memory of
Harry Lehmann
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