Results 41 to 50 of about 160,813 (290)

Scattering forms and the positive geometry of kinematics, color and the worldsheet

Journal of High Energy Physics, 2018
The search for a theory of the S-Matrix over the past five decades has revealed surprising geometric structures underlying scattering amplitudes ranging from the string worldsheet to the amplituhedron, but these are all geometries in auxiliary spaces as ...
Nima Arkani-Hamed, Yuntao Bai, Song He, Gongwang Yan   +3 more
doaj   +1 more source

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
doaj   +1 more source

Tropical fans, scattering equations and amplitudes

Journal of High Energy Physics, 2021
We describe a family of tropical fans related to Grassmannian cluster algebras. These fans are related to the kinematic space of massless scattering processes in a number of ways.
James Drummond, Jack Foster, Ömer Gürdoğan, Chrysostomos Kalousios   +3 more
doaj   +1 more source

The fundamental theorem of tropical partial differential algebraic geometry [PDF]

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, 2020
20 pages, 2 figures.
Falkensteiner, Sebastian, Garay-López, Cristhian, Haiech, Mercedes, Noordman, Marc Paul, Toghani, Zeinab, Boulier, François   +5 more
openaire   +3 more sources

Multidimensional Toda type systems [PDF]

, 1996
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear systems is obtained, and the integration scheme for such equations is proposed.Comment: 29 pages, LaTeX ...
A. N. Leznov, A. V. Razumov, A. V. Razumov, A. V. Razumov, B. Dubrovin, C.-L. Terng, G. Darboux, J. E. Humphreys, J.-L. Gervais, J.-L. Gervais, K. Tenenblat, L. A. Ferreira, L. Bianchi, L. Fehér, M. J. Ablowitz, M. Sato, M. V. Saveliev, M. V. Saveliev, N. Bourbaki, S. Cecotti, S. Cecotti, V. E. Korepin, Yu. A. Aminov   +22 more
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Scattering forms, worldsheet forms and amplitudes from subspaces

Journal of High Energy Physics, 2018
We present a general construction of two types of differential forms, based on any (n−3)-dimensional subspace in the kinematic space of n massless particles.
Song He, Gongwang Yan, Chi Zhang, Yong Zhang   +3 more
doaj   +1 more source

On positive geometries of quartic interactions: Stokes polytopes, lower forms on associahedra and world-sheet forms

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, Pinaki Banerjee, Mrunmay Jagadale, Renjan Rajan John, Alok Laddha, Sujoy Mahato   +5 more
doaj   +1 more source

Adjoint orbits, generalised parallelisable spaces and consistent truncations

Journal of High Energy Physics, 2019
The aim of this note is to present some new explicit examples of O(d, d)generalised Leibniz parallelisable spaces arising as the normal bundles of adjoint orbits O $$ \mathcal{O} $$ of some semi-simple Lie group G.
Louise Anderson
doaj   +1 more source

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
doaj   +1 more source

Rationality in Differential Algebraic Geometry [PDF]

, 2015
Abel Symposium ...
openaire   +3 more sources