论文标题
质量双曲线作为泊松小组
The Mass Hyperboloid as a Poisson-Lie Group
论文作者
论文摘要
Dirac显示出具有许多优势的巨大标量场的光锥形式主义。但这并不是洛伦兹不变的。我们将证明这不是一个功能：洛伦兹的不变性确实是一种对称性，而是由Drinfel定义的不同意义。关键的想法是，质量壳（质量双曲线）是一个泊松群体：在四弹药的组件之间有一个非亚伯群乘法和非零泊松支架。从drinfel的意义上讲，旋转形成了双曲线的双重组。无穷小的洛伦兹变换形成了双方代数。
The light cone formalism of a massive scalar field has been shown by Dirac to have many advantages. But it is not manifestly Lorentz invariant. We will show that this is a feature not a bug: Lorentz invariance is indeed a symmetry, but in a different sense defined by Drinfel'd. The key idea is that the mass shell (mass hyperboloid) is a Poisson-Lie group: there is a non-abelian group multiplication and non-zero Poisson brackets between components of four-momentum. Rotations form the dual group of the hyperboloid in the sense of Drinfel'd. Infinitesimal Lorentz transformations form a Lie bi-algebra.
