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Algebraic aspects of hypergeometric differential equations [PDF]
Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, 2020 We review some classical and modern aspects of hypergeometric differential equations, including A-hypergeometric systems of Gel′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{
Thomas Reichelt +3 more
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Weights and recursion relations for ϕ p tree amplitudes from the positive geometry
Journal of High Energy Physics, 2020 Recently, the accordiohedron in kinematic space was proposed as the positive geometry for planar tree-level scattering amplitudes in the ϕ p theory [1]. The scattering amplitudes are given as a weighted sum over canonical forms of some accordiohedra with
Ryota Kojima
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Notes on biadjoint amplitudes, Trop G(3, 7) and X(3, 7) scattering equations
Journal of High Energy Physics, 2020 In these notes we use the recently found relation between facets of tropical Grassmannians and generalizations of Feynman diagrams to compute all “biadjoint amplitudes” for n = 7 and k = 3.
Freddy Cachazo, Jairo M. Rojas
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Kinematic singularities of Feynman integrals and principal A-determinants
Journal of High Energy Physics, 2022 We consider the analytic properties of Feynman integrals from the perspective of general A-discriminants and A $$ \mathcal{A} $$ -hypergeometric functions introduced by Gelfand, Kapranov and Zelevinsky (GKZ).
René Pascal Klausen
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Journal of High Energy Physics, 2020 In [1], two of the present authors along with P. Raman attempted to extend the Amplituhedron program for scalar field theories [2] to quartic scalar interactions. In this paper we develop various aspects of this proposal.
P.B. Aneesh +5 more
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Differential algebra (contravariant analytic methods in differential geometry) [PDF]
Journal of Soviet Mathematics, 1980 The problems of developing the apparatus of differential-geometric investigations based on the calculus of differential operators on bundles of semiholonomic jets of Ehresmann are considered.
A. M. Vasil'ev
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Differential-algebraic systems are generically controllable and stabilizable
MCSS. Mathematics of Control, Signals and Systems, 2021 We investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in ...
A. Ilchmann, Jonas Kirchhoff
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Anyons in geometric models of matter
Journal of High Energy Physics, 2017 We show that the “geometric models of matter” approach proposed by the first author can be used to construct models of anyon quasiparticles with fractional quantum numbers, using 4-dimensional edge-cone orbifold geometries with orbifold singularities ...
Michael Atiyah, Matilde Marcolli
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Current Algebra and Differential Geometry
Journal of High Energy Physics, 2005 14 pages. Dedicated to Ludwig Faddeev on the occasion of his 70th birthday.
Alekseev, Anton, Strobl, Thomas
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Schubert problems, positivity and symbol letters
Journal of High Energy Physics, 2022 We propose a geometrical approach to generate symbol letters of amplitudes/integrals in planar N $$ \mathcal{N} $$ = 4 Super Yang-Mills theory, known as Schubert problems. Beginning with one-loop integrals, we find that intersections of lines in momentum
Qinglin Yang
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