Topic
Product (mathematics)
About: Product (mathematics) is a research topic. Over the lifetime, 44382 publications have been published within this topic receiving 377809 citations.
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TL;DR: In this paper, a polytope picture for scattering amplitudes in generalized momentum-twistor spaces is presented, where amplitudes are associated with the volumes of polytopes.
Abstract: In this note we continue the exploration of the polytope picture for scattering amplitudes, where amplitudes are associated with the volumes of polytopes in generalized momentum-twistor spaces. After a quick warm-up example illustrating the essential ideas with the elementary geometry of polygons in $ \mathbb{C}{\mathbb{P}^{{2}}} $
, we interpret the 1-loop MHV integrand as the volume of a polytope in $ \mathbb{C}{\mathbb{P}^{{3}}} $
× $ \mathbb{C}{\mathbb{P}^{{3}}} $
, which can be thought of as the space obtained by taking the geometric dual of the Wilson loop in each $ \mathbb{C}{\mathbb{P}^{{3}}} $
of the product. We then review the polytope picture for the NMHV tree amplitude and give it a more direct and intrinsic definition as the geometric dual of a canonical “square” of the Wilson-Loop polygon, living in a certain extension of momentum-twistor space into $ \mathbb{C}{\mathbb{P}^{{4}}} $
. In both cases, one natural class of triangulations of the polytope produces the BCFW/CSW representations of the amplitudes; another class of triangulations leads to a striking new form, which is both remarkably simple as well as manifestly cyclic and local.
136 citations
136 citations
TL;DR: In this paper, two studies on how negative country images can be removed by investigating the effects of decomposing country image into component and assembly origins, as well as the effects on component origins.
Abstract: This article reports two studies on how negative country images can be removed by investigating the effects of decomposing country image into component and assembly origins, as well as the effects ...
136 citations
TL;DR: In this article, the properties of the Golden structure on a manifold were investigated by using a corresponding almost product structure, where the Golden proportion plays a central role in the geometry of the manifold.
Abstract: A research on the properties of the Golden structure (i.e. a polynomial structure with the structure polynomial Q ( X ) = X 2 - X - I ) is carried out in this article. The Golden proportion plays a central role in this paper. The geometry of the Golden structure on a manifold is investigated by using a corresponding almost product structure.
135 citations
TL;DR: In this paper, a star product associated with an arbitrary two-dimensional Poisson structure using generalized coherent states on the complex plane is constructed for the fuzzy torus and fuzzy sphere.
134 citations