Results 81 to 90 of about 2,492,523 (198)

Manifest symplecticity in classical scattering

Journal of High Energy Physics
The Liouville theorem states that classical time evolution is an incompressible flow in phase space. We investigate two formulations of classical mechanics in which this property is manifested. First, the traditional Hamilton-Jacobi theory provides an in-
Joon-Hwi Kim
doaj   +1 more source

Multi-linear Formulation of Differential Geometry and Matris Regularizations

, 2012
We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi-linear algebraic structures on the space of smooth functions.
Hoppe, Jens,, Arnlind, Joakim,, Huisken, Gerhard,   +2 more
core  

Algebraic geometry and local differential geometry [PDF]

Annales scientifiques de l'École normale supérieure, 1979
Griffiths, Phillip, Harris, Joseph
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Self-duality from twisted cohomology

Journal of High Energy Physics
Recently a notion of self-duality for differential equations of maximal cuts was introduced, which states that there should be a basis in which the matrix for an ε-factorised differential equation is persymmetric.
Claude Duhr, Franziska Porkert, Cathrin Semper, Sven F. Stawinski   +3 more
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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

Algebraic geometry proceedings of Bilkent Summer School

, 1997
This timely resource - based on the Summer School on Algebraic Geometry held recently at Bilkent University, Ankara, Turkey - surveys and applies fundamental ideas and techniques in the theory of curves, surfaces, and threefolds to a wide variety of ...
Algebraic Geometry Summer School 1995 Ankara, Sertöz, Sinan   +1 more
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Free integro-differential algebras and Groebner-Shirshov bases [PDF]

, 2014
The notion of commutative integro-differential algebra was introduced for the algebraic study of boundary problems for linear ordinary differential equations. Its noncommutative analog achieves a similar purpose for linear systems of such equations.
Guo, Li, Gao, Xing, Rosenkranz, Markus, Markus Rosenkranz, Li Guo, Xing Gao   +5 more
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A Calabi-Yau-to-curve correspondence for Feynman integrals

Journal of High Energy Physics
It has long been known that the maximal cut of the equal-mass four-loop banana integral is a period of a family of Calabi-Yau threefolds that depends on the kinematic variable z = m 2/p 2.
Hans Jockers, Sören Kotlewski, Pyry Kuusela, Andrew J. McLeod, Sebastian Pögel, Maik Sarve, Xing Wang, Stefan Weinzierl   +7 more
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Nonsmooth differential geometry and algebras of generalized functions

Journal of Mathematical Analysis and Applications, 2004
17 pages, typos ...
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Topics in algebra, geometry and differential equations

, 2022
The study of differential equations and the study of algebraic geometry are two disciplines within mathematics that seem to be mostly disjoint from each other. Looking deeper, however, one finds that connections do exist. This thesis gives in four chapters four examples of interesting mathematical insights that can be gained from combining the concepts
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