The lightcone singularity at the origin is resolved by blowing up the singular point to $\mathbb{C}{P}^1$. The Lorentz group acts on the resolved lightcone and has $\mathbb{C}{P}^1$ as a special orbit. Using Wigner's method of associating unitary irreducible representations of the Poincaré group to particle states, we find that the special orbit gives rise to new vacuum states. These vacuum states are labeled by the principal series representations of $SL(2,\mathbb{C})$. Some remarks are included on the applications of these results to gauge theories and asymptotically flat spacetimes.

中文翻译：

---

光锥奇点分辨率的真空态

原点的光锥奇点是通过将奇点炸开来解决的 $\mathbb{C}{磷}^1$. 洛伦兹群作用于解析出的光锥，并有$\mathbb{C}{磷}^1$作为一个特殊的轨道。使用 Wigner 将庞加莱群的幺正不可约表示与粒子状态相关联的方法，我们发现特殊轨道会产生新的真空状态。这些真空状态由以下的主要级数表示标记$秒升(2,\mathbb{C})$. 包括一些关于将这些结果应用于规范理论和渐近平坦时空的评论。