无质量粒子的运动学变量

arXiv - MATH - Algebraic Geometry Pub Date : 2024-08-29 DOI:arxiv-2408.16711

Smita Rajan, Svala Sverrisdóttir, Bernd Sturmfels

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引用次数: 0

摘要

我们研究在动量守恒条件下，编码 $d$ 维时空中 $n$ 无质量粒子运动数据的代数变量。它们的坐标是旋子括号，我们从与洛伦兹群相关的克利福德代数中推导出旋子括号。这是在最近的物理学文献中针对 $d=5$ 提出的。我们的运动学变量是由具有对称和倾斜对称切片的多项式张量约束给出的。

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Kinematic Varieties for Massless Particles

We study algebraic varieties that encode the kinematic data for $n$ massless particles in $d$-dimensional spacetime subject to momentum conservation. Their coordinates are spinor brackets, which we derive from the Clifford algebra associated to the Lorentz group. This was proposed for $d=5$ in the recent physics literature. Our kinematic varieties are given by polynomial constraints on tensors with both symmetric and skew symmetric slices.

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arXiv - MATH - Algebraic Geometry

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