Results 41 to 50 of about 164,069 (206)
Hyperbolic geometry and amplituhedra in 1+2 dimensions
Journal of High Energy Physics, 2018 Recently, the existence of an Amplituhedron for tree level amplitudes in the bi-adjoint scalar field theory has been proved by Arkani-Hamed et al.
G. Salvatori, S. L. Cacciatori
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Holonomic representation of biadjoint scalar amplitudes
Journal of High Energy Physics, 2023 We study tree-level biadjoint scalar amplitudes in the language of D-modules. We construct left ideals in the Weyl algebra D that allow a holonomic representation of n-point amplitudes in terms of the linear partial differential equations they satisfy ...
Leonardo de la Cruz
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Examples of noncommutative manifolds: complex tori and spherical manifolds
, 2007 We survey some aspects of the theory of noncommutative manifolds focusing on the noncommutative analogs of two-dimensional tori and low-dimensional spheres. We are particularly interested in those aspects of the theory that link the differential geometry
Plazas, Jorge
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Algebraic branch points at all loop orders from positive kinematics and wall crossing
Journal of High Energy Physics, 2021 There is a remarkable connection between the boundary structure of the positive kinematic region and branch points of integrated amplitudes in planar N $$ \mathcal{N} $$ = 4 SYM.
Aidan Herderschee
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GEOMETRIC AND EXTENSOR ALGEBRAS AND THE DIFFERENTIAL GEOMETRY OF ARBITRARY MANIFOLDS [PDF]
International Journal of Geometric Methods in Modern Physics, 2007 We give in this paper which is the third in a series of four a theory of covariant derivatives of representatives of multivector and extensor fields on an arbitrary open set U ⊂ M, based on the geometric and extensor calculus on an arbitrary smooth manifold M.
Fernández, V. V. +2 more
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Cutting the traintracks: Cauchy, Schubert and Calabi-Yau
Journal of High Energy Physics, 2023 In this note we revisit the maximal-codimension residues, or leading singularities, of four-dimensional L-loop traintrack integrals with massive legs, both in Feynman parameter space and in momentum (twistor) space.
Qu Cao, Song He, Yichao Tang
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Tropical Grassmannians, cluster algebras and scattering amplitudes
Journal of High Energy Physics, 2020 We provide a cluster-algebraic approach to the computation of the recently introduced generalised biadjoint scalar amplitudes related to Grassmannians Gr(k, n). A finite cluster algebra provides a natural triangulation for the tropical Grassmannian whose
James Drummond +3 more
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Towards analytic structure of Feynman parameter integrals with rational curves
Journal of High Energy Physics, 2022 We propose a strategy to study the analytic structure of Feynman parameter integrals where singularities of the integrand consist of rational irreducible components.
Jianyu Gong, Ellis Ye Yuan
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Thom series of contact singularities [PDF]
, 2010 Thom polynomials measure how global topology forces singularities. The power of Thom polynomials predestine them to be a useful tool not only in differential topology, but also in algebraic geometry (enumerative geometry, moduli spaces) and algebraic ...
Fehér, L. M., Rimányi, R.
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Lectures on Graded Differential Algebras and Noncommutative Geometry [PDF]
, 2001 These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new developments.
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