Results 51 to 60 of about 7,630 (283)

Scattering equations: from projective spaces to tropical grassmannians

Journal of High Energy Physics, 2019
We introduce a natural generalization of the scattering equations, which connect the space of Mandelstam invariants to that of points on ℂℙ1, to higher-dimensional projective spaces ℂℙ k − 1.
Freddy Cachazo, Nick Early, Alfredo Guevara, Sebastian Mizera   +3 more
doaj   +1 more source

Discrete exterior geometry approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems [PDF]

, 2011
This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce a simplicial Dirac structure as a discrete analogue
Seslija, Marko,, Scherpen, Jacquelien M.A.,, van der Schaft, Abraham, van der Schaft, Abraham; id_orcid, Arjan Van Der Schaft, Jacquelien M. A. Scherpen, van der Schaft, Arjan, Scherpen, Jacquelien M.A., Seslija, Marko, van der Schaft, Arjan ; id_orcid, Marko Seslija, Schaft, Arjan van der,   +11 more
core   +3 more sources

Special geometry on the 101 dimesional moduli space of the quintic threefold

Journal of High Energy Physics, 2018
A new method for explicit computation of the CY moduli space metric was proposed by the authors recently. The method makes use of the connection of the moduli space with a certain Frobenius algebra.
Konstantin Aleshkin, Alexander Belavin
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

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., Moya, A. M., Rodrigues, W. A. jun.   +2 more
openaire   +3 more sources

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

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
doaj   +1 more source

Differential Geometry Revisited by Biquaternion Clifford Algebra [PDF]

, 2015
In the last century, differential geometry has been expressed within various calculi: vectors, tensors, spinors, exterior differential forms and recently Clifford algebras. Clifford algebras yield an excellent representation of the rotation group and of the Lorentz group which are the cornerstones of the theory of moving frames.
Girard, Patrick, Clarysse, Patrick, Pujol, Romaric, Wang, Liang, Delachartre, Philippe   +4 more
openaire   +4 more sources

Artificial Intelligence Meets Micro/Nanorobotics

Advanced Materials, EarlyView.
Artificial intelligence is transforming micro‐ and nanorobots from externally controlled, task‐specific machines into adaptive, autonomous systems. Machine learning, multimodal perception, digital twins, AI‐guided materials and geometry design enhance propulsion, localization, decision‐making, whichaccelerates clinical and environmental applications ...
Fatma M. Yurtsever, Minitha Cherukutty Ramakrishnan, Ian Kuula Ross, Ivan Zelinka, Hamed Shahsavan, Michal Otyepka, Martin Pumera   +6 more
wiley   +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