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 N$^3$LO, 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 Economía y Competitividad TIN2016-75394-RMinisterio de Ciencia e Innovación PID2020-112540RB-C44Junta de Andalucía P18-RT-1060Junta de Andalucía US-138137