论文标题
庞加莱集团的多粒子表示
Multi-particle Representations of the Poincaré Group
论文作者
论文摘要
在这项工作中，我们扩展了$ s $ matrix的渐近多粒子状态的定义，超出了单粒子状态的直接产物。我们确定与渐近分离的粒子对相关的新量子数，或称为成对的螺旋度或$ q_ {ij} $。这些信号表明，除了轨道和自旋贡献之外，角度动量的新来源的外观。我们的结构的本质是首先独立处理所有单个颗粒以及所有粒子对，最终投射到物理状态上。由此产生的表示形式重现了通常的直接产品状态，以消失$ q_ {ij} $，而为了消失旋转，它们会繁殖Zwanziger的电力磁性多粒子状态。然后，除了标准的小组变换外，成对的螺旋度除了它们的标准小组变换外，还显示了我们量子状态的额外小组阶段的标签。我们新定义的多粒子状态是电荷散射的正确渐近状态，成对的螺旋度确定为$ q_ {ij} = e_i g_j-e_j g_i $。
In this work we extend the definition of asymptotic multi-particle states of the $S$-matrix, beyond the direct products of one-particle states. We identify new quantum numbers which we call pairwise helicities, or $q_{ij}$, associated with asymptotically separated pairs of particles. These signal the appearance of a new source of angular momentum, beyond the orbital and spin contributions. The essence of our construction is to first treat all single particles as well as all particle pairs independently, ultimately projecting onto the physical states. The resulting representations reproduce the usual direct product states for vanishing $q_{ij}$, while for vanishing spins they reproduce Zwanziger's electric-magnetic multi-particle states. Pairwise helicity then appears as a label for the extra little group phase for our quantum states, in addition to their standard little group transformation. Our newly defined multi-particle states are the correct asymptotic states for the scattering of electric and magnetic charges, with pairwise helicity identified as $q_{ij}=e_i g_j-e_j g_i$.
