811 research outputs found
Enumeration of N-rooted maps using quantum field theory
A one-to-one correspondence is proved between the N-rooted ribbon graphs, or
maps, with e edges and the (e-N+1)-loop Feynman diagrams of a certain quantum
field theory. This result is used to obtain explicit expressions and relations
for the generating functions of N-rooted maps and for the numbers of N-rooted
maps with a given number of edges using the path integral approach applied to
the corresponding quantum field theory.Comment: 27 pages, 7 figure
Feynman diagrams, ribbon graphs, and topological recursion of Eynard-Orantin
We consider two seemingly unrelated problems, the calculation of the WKB
expansion of the harmonic oscillator wave functions and the counting the number
of Feynman diagrams in QED or in many-body physics and show that their
solutions are both encoded in a single enumerative problem, the calculation of
the number of certain types of ribbon graphs. In turn, the numbers of such
ribbon graphs as a function of the number of their vertices and edges can be
determined recursively through the application of the topological recursion of
Eynard-Orantin to the algebraic curve encoded in the Schr\"odinger equation of
the harmonic oscillator. We show how the numbers of these ribbon graphs can be
written down in closed form for any given number of vertices and edges. We use
these numbers to obtain a formula for the number of N-rooted ribbon graphs with
e edges, which is the same as the number of Feynman diagrams for 2N-point
function with e+1-N loops.Comment: 29 pages, 7 figure
Brandon LaBelle and Konstantinos Thomaidis: Vocal Positionings
This Salon conversation/podcast explores sound and meaning, the performativity of the self in listening and voicing, aural dramaturgies of inclusion/exclusion, and the intersections of history, politics and voice. It features excerpts from James Webbâs sound work A Series of Personal Questions Addressed to 5 Litres of Nigerian Crude Oil (2015) and from Thomaidisâs own autobiophonic piece A Voice Is. A Voice Has. A Voice Does (2018)
The collaborative process of sustainable innovations under the lens of actorânetwork theory
The development of sustainable innovation (SI) is complex and risky due to the characteristics and diversity of actors involved in its process. Little is known about the collaborative process underlying this development. The objective of the paper is to explore the collaborative mechanisms and dynamics that influence the process and characteristics of sustainable innovations. The translation approach of the actorânetwork theory is applied to shed light on the collaborative process of two cases of sustainable innovations within small-and medium-sized enterprises. The sociotechnical graph method is used as a methodology to track the mechanisms and compare the dynamics of their processes. The results reveal that the governance characteristic of sustainable innovations and the moment of mobilization are essential aspects of the collaborative processes. They show that, depending on the intensity and systemic impacts of SI, attraction and retention are important mechanisms in the construction of the governance characteristics of SI. A manager who uses these mechanisms during the mobilization of actors, having resources related to the governance characteristics, succeeds in sustainable innovation development. The paper contributes to the literature on sustainability management by linking the âbecomingâ of sustainable innovations to their collaborative processes. It also informs managers on how to manage the collaborative process of sustainable innovations by relying on a translation approach. © 2021 by the authors. Licensee MDPI, Basel, Switzerland
The flavor symmetry in the standard model and the triality symmetry
A Dirac fermion is expressed by a 4 component spinor which is a combination
of two quaternions and which can be treated as an octonion. The octonion
possesses the triality symmetry, which defines symmetry of fermion spinors and
bosonic vector fields.
The triality symmetry relates three sets of spinors and two sets of vectors,
which are transformed among themselves via transformations , and . If the electromagnetic (EM) interaction is
sensitive to the triality symmetry, i.e. EM probe selects one triality sector,
EM signals from the 5 transformed world would not be detected, and be treated
as the dark matter. According to an astrophysical measurement, the ratio of the
dark to ordinary matter in the universe as a whole is almost exactly 5. We
expect quarks are insensitive to the triality, and triality will appear as
three times larger flavor degrees of freedom in the lattice simulation.Comment: 16 pages 8 figures, To be published in International Journal of
Modern Physics
Searching for New Physics in Leptonic Decays of Bottomonium
New Physics can show up in various well-known processes already studied in
the Standard Model, in particular by modifying decay rates to some extent. In
this work, I examine leptonic decays of vector resonances of
bottomonium below production, subsequent to a magnetic dipole
radiative structural transition of the vector resonance yielding a pseudoscalar
continuum state, searching for the existence of a light Higgs-like neutral
boson that would imply a slight but experimentally measurable breaking of
lepton universality.Comment: LaTeX, 12 pages, 1 EPS figur
Division Algebras and Extended N=2,4,8 SuperKdVs
The first example of an N=8 supersymmetric extension of the KdV equation is
here explicitly constructed. It involves 8 bosonic and 8 fermionic fields. It
corresponds to the unique N=8 solution based on a generalized hamiltonian
dynamics with (generalized) Poisson brackets given by the Non-associative N=8
Superconformal Algebra. The complete list of inequivalent classes of
parametric-dependent N=3 and N=4 superKdVs obtained from the ``Non-associative
N=8 SCA" is also furnished. Furthermore, a fundamental domain characterizing
the class of inequivalent N=4 superKdVs based on the "minimal N=4 SCA" is
given.Comment: 14 pages, LaTe
Breit Hamiltonian and QED Effects for Spinless Particles
We describe a simplified derivation for the relativistic corrections of order
for a bound system consisting of two spinless particles. We devote
special attention to pionium, the bound system of two oppositely charged pions.
The leading quantum electrodynamic (QED) correction to the energy levels is of
the order of and due to electronic vacuum polarization. We analyze
further corrections due to the self-energy of the pions, and due to recoil
effects, and we give a complete result for the scalar-QED leading logarithmic
corrections which are due to virtual loops involving only the scalar
constituent particles (the pions); these corrections are of order for S states.Comment: 12 pages, LaTeX; references added (J. Phys. B, in press
Bregman Voronoi Diagrams: Properties, Algorithms and Applications
The Voronoi diagram of a finite set of objects is a fundamental geometric
structure that subdivides the embedding space into regions, each region
consisting of the points that are closer to a given object than to the others.
We may define many variants of Voronoi diagrams depending on the class of
objects, the distance functions and the embedding space. In this paper, we
investigate a framework for defining and building Voronoi diagrams for a broad
class of distance functions called Bregman divergences. Bregman divergences
include not only the traditional (squared) Euclidean distance but also various
divergence measures based on entropic functions. Accordingly, Bregman Voronoi
diagrams allow to define information-theoretic Voronoi diagrams in statistical
parametric spaces based on the relative entropy of distributions. We define
several types of Bregman diagrams, establish correspondences between those
diagrams (using the Legendre transformation), and show how to compute them
efficiently. We also introduce extensions of these diagrams, e.g. k-order and
k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set
of points and their connexion with Bregman Voronoi diagrams. We show that these
triangulations capture many of the properties of the celebrated Delaunay
triangulation. Finally, we give some applications of Bregman Voronoi diagrams
which are of interest in the context of computational geometry and machine
learning.Comment: Extend the proceedings abstract of SODA 2007 (46 pages, 15 figures
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