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Restrictions of Pfaffian systems for Feynman integrals
Journal of High Energy Physics, 2023 This work studies limits of Pfaffian systems, a class of first-order PDEs appearing in the Feynman integral calculus. Such limits appear naturally in the context of scattering amplitudes when there is a separation of scale in a given set of kinematic ...
Vsevolod Chestnov +3 more
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Differential algebras in non-commutative geometry [PDF]
Journal of Geometry and Physics, 1995 We discuss the differential algebras used in Connes' approach to Yang-Mills theories with spontaneous symmetry breaking. These differential algebras generated by algebras of the form functions $\otimes$ matrix are shown to be skew tensorproducts of differential forms with a specific matrix algebra.
Kalau, W. +3 more
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Tensor Triangular Geometry of Differential Graded Algebras
This paper explores the intricate relationship between tensor triangular geometry and the theory of differential graded algebras (DGAs). DGAs provide a powerful framework for extending classical algebraic structures, incorporating homological information crucial for applications in algebraic topology, algebraic geometry, and representation theory ...
SÉRGIO DE ANDRADE, PAULO
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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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Poisson algebras via model theory and differential-algebraic geometry [PDF]
Journal of the European Mathematical Society, 2017 Brown and Gordon asked whether the Poisson Dixmier–Moeglin equivalence holds for any complex affine Poisson algebra, that is, whether the sets of Poisson rational ideals, Poisson primitive ideals, and Poisson locally closed ideals coincide. In this article a complete answer is given to this question using techniques from differential-algebraic geometry
Bell, Jason +3 more
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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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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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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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