What is the Amplituhedron
What is the Amplituhedron
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DOI：
10.1090/noti1630
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发表时间：
2018-02
影响因子：
--
通讯作者：
J. Bourjaily;H. Thomas
中科院分区：
文献类型：
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作者：
J. Bourjaily;H. Thomas
散射振幅是量子场论的基础。空间和时间是现实的基本组成部分......"在这篇简短的文章中，我们不会挑战空间和时间的概念，但我们将对物理学和数学中的振幅面体的性质和意义给出一些解释，它是作为格拉斯曼主义者对总积极性的自然概括而出现的。让我们开始从散射振幅物理学中这些想法的起源开始。对于任何特定的量子场理论，一定数量的粒子“散射”并产生一定数量的其他粒子的概率由该过程的称为（散射）振幅的函数编码。这些函数依赖于所有可观测到的数字，这些数字标记了这个过程中所涉及的状态，特别是动量和螺旋度。振幅可以（经常）根据费曼“环”展开微扰确定。在领导秩序上，他们是理性的
Scattering amplitudes are the bread and butter of quantum field theory. notion that space and time are fundamental components of reality...” In this short article, we will not get as far as challenging the notions of space and time, but we will give some explanation as to the nature and significance of the amplituhedron both in physics and mathematics—where it arises as a natural generalization of the subject of total positivity for Grassmannians. Let us begin with the origin of these ideas in the physics of scattering amplitudes. For any particular quantumfield theory, the probability for some number of particles to ‘scatter’ and produce some number of others is encoded by a function called the (scattering) amplitude for that process. These functions depend on all the observable numbers labeling the states involved in the process—in particular, momenta and helicity. Amplitudes can (often) be determined perturbatively according to the Feynman ‘loop’ expansion. At leading order, they are rational