Kinematic Varieties for Massless Particles

TL;DR

This paper investigates algebraic varieties representing the kinematic data of multiple massless particles in various dimensions, using spinor brackets derived from Clifford algebra, and describes their polynomial constraints.

Contribution

It introduces a new algebraic geometric framework for massless particle kinematics in arbitrary dimensions, extending previous work limited to specific cases.

Findings

Defines kinematic varieties via polynomial constraints on tensors.

Derives spinor bracket coordinates from Clifford algebra.

Generalizes the algebraic structure for massless particles in different dimensions.

Abstract

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.