423 research outputs found
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
Localization and the interface between quantum mechanics, quantum field theory and quantum gravity I (The two antagonistic localizations and their asymptotic compatibility)
It is shown that there are significant conceptual differences between QM and
QFT which make it difficult to view the latter as just a relativistic extension
of the principles of QM. At the root of this is a fundamental distiction
between Born-localization in QM (which in the relativistic context changes its
name to Newton-Wigner localization) and modular localization which is the
localization underlying QFT, after one separates it from its standard
presentation in terms of field coordinates. The first comes with a probability
notion and projection operators, whereas the latter describes causal
propagation in QFT and leads to thermal aspects of locally reduced finite
energy states. The Born-Newton-Wigner localization in QFT is only applicable
asymptotically and the covariant correlation between asymptotic in and out
localization projectors is the basis of the existence of an invariant
scattering matrix. In this first part of a two part essay the modular
localization (the intrinsic content of field localization) and its
philosophical consequences take the center stage. Important physical
consequences of vacuum polarization will be the main topic of part II. Both
parts together form a rather comprehensive presentation of known consequences
of the two antagonistic localization concepts, including the those of its
misunderstandings in string theory.Comment: 63 pages corrections, reformulations, references adde
Set-Valued Analysis
This Special Issue contains eight original papers with a high impact in various domains of set-valued analysis. Set-valued analysis has made remarkable progress in the last 70 years, enriching itself continuously with new concepts, important results, and special applications. Different problems arising in the theory of control, economics, game theory, decision making, nonlinear programming, biomathematics, and statistics have strengthened the theoretical base and the specific techniques of set-valued analysis. The consistency of its theoretical approach and the multitude of its applications have transformed set-valued analysis into a reference field of modern mathematics, which attracts an impressive number of researchers
The 2nd International Conference on Mathematical Modelling in Applied Sciences, ICMMAS’19, Belgorod, Russia, August 20-24, 2019 : book of abstracts
The proposed Scientific Program of the conference is including plenary lectures, contributed oral talks, poster sessions and listeners. Five suggested special sessions / mini-symposium are also considered by the scientific committe
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