6,176 research outputs found
String states, loops and effective actions in noncommutative field theory and matrix models
Refining previous work by Iso, Kawai and Kitazawa, we discuss bi-local string
states as a tool for loop computations in noncommutative field theory and
matrix models. Defined in terms of coherent states, they exhibit the stringy
features of noncommutative field theory. This leads to a closed form for the
1-loop effective action in position space, capturing the long-range non-local
UV/IR mixing for scalar fields. The formalism applies to generic fuzzy spaces.
The non-locality is tamed in the maximally supersymmetric IKKT or IIB model,
where it gives rise to supergravity. The linearized supergravity interactions
are obtained directly in position space at one loop using string states on
generic noncommutative branes.Comment: 31 pages, 2 figure
The Principle of Locality. Effectiveness, fate and challenges
The Special Theory of Relativity and Quantum Mechanics merge in the key
principle of Quantum Field Theory, the Principle of Locality. We review some
examples of its ``unreasonable effectiveness'' (which shows up best in the
formulation of Quantum Field Theory in terms of operator algebras of local
observables) in digging out the roots of Global Gauge Invariance in the
structure of the local observable quantities alone, at least for purely massive
theories; but to deal with the Principle of Local Gauge Invariance is still a
problem in this frame. This problem emerges also if one attempts to figure out
the fate of the Principle of Locality in theories describing the gravitational
forces between elementary particles as well. Spacetime should then acquire a
quantum structure at the Planck scale, and the Principle of Locality is lost.
It is a crucial open problem to unravel a replacement in such theories which is
equally mathematically sharp and reduces to the Principle of Locality at larger
scales. Besides exploring its fate, many challenges for the Principle of
Locality remain; among them, the analysis of Superselection Structure and
Statistics also in presence of massless particles, and to give a precise
mathematical formulation to the Measurement Process in local and relativistic
terms; for which we outline a qualitative scenario which avoids the EPR
Paradox.Comment: 36 pages. Survey partially based on a talk delivered at the Meeting
"Algebraic Quantum Field Theory: 50 years", Goettingen, July 29-31, 2009, in
honor of Detlev Buchholz. Submitted to Journal of Mathematical Physic
Nuclear Physics without High-Momentum Potentials: Constructing the Nuclear Effective Interaction Directly from Scattering Observables
The traditional approach to nuclear physics encodes phase shift information
in a nucleon-nucleon (NN) potential, producing a nucleon-level interaction that
captures the sub-GeV consequences of QCD. A further reduction to the nuclear
scale is needed to produce an effective interaction for soft Hilbert spaces,
such as those employed in the shell model. Here we describe an alternative
construction of this effective interaction, from QCD directly to the nuclear
scale, that is direct and precise. This eliminates the need for constructing
and renormalizing the high-momentum NN potential. Instead, continuum phase
shifts and mixing angles are used directly at the nuclear scale. The method
exploits the analytic continuity in energy of HOBET (Harmonic-Oscillator-Based
Effective Theory) to connect bound states to continuum solutions at specific
energies. The procedure is systematic, cutoff independent, and convergent,
yielding keV accuracy at NNLO or NLO, depending on the channel. Lepage
plots are provided.Comment: 9 page
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
Continuous selections of multivalued mappings
This survey covers in our opinion the most important results in the theory of
continuous selections of multivalued mappings (approximately) from 2002 through
2012. It extends and continues our previous such survey which appeared in
Recent Progress in General Topology, II, which was published in 2002. In
comparison, our present survey considers more restricted and specific areas of
mathematics. Note that we do not consider the theory of selectors (i.e.
continuous choices of elements from subsets of topological spaces) since this
topics is covered by another survey in this volume
On exploring data lakes by finding compact, isolated clusters
Data engineers are very interested in data lake technologies due to the incredible abun dance of datasets. They typically use clustering to understand the structure of the datasets
before applying other methods to infer knowledge from them. This article presents the first
proposal that explores how to use a meta-heuristic to address the problem of multi-way
single-subspace automatic clustering, which is very appropriate in the context of data
lakes. It was confronted with five strong competitors that combine the state-of-the-art
attribute selection proposal with three classical single-way clustering proposals, a recent
quantum-inspired one, and a recent deep-learning one. The evaluation focused on explor ing their ability to find compact and isolated clusterings as well as the extent to which such
clusterings can be considered good classifications. The statistical analyses conducted on
the experimental results prove that it ranks the first regarding effectiveness using six stan dard coefficients and it is very efficient in terms of CPU time, not to mention that it did not
result in any degraded clusterings or timeouts. Summing up: this proposal contributes to
the array of techniques that data engineers can use to explore their data lakesMinisterio de EconomÃa y Competitividad TIN2016-75394-RMinisterio de Ciencia e Innovación PID2020-112540RB-C44Junta de AndalucÃa P18-RT-1060Junta de AndalucÃa US-138137
- …