We extend the definition of asymptotic multiparticle states of the $S$-matrix beyond the tensor products of one-particle states. We identify new quantum numbers called pairwise helicities, or $q_{ij}$, associated with asymptotically separated pairs of particles. We first treat all single particles and particle pairs independently, allowing us to generalize the Wigner construction, and ultimately projecting onto the physical states. Our states reduce to tensor product states for vanishing $q_{ij}$, while for vanishing spins they reproduce Zwanziger’s scalar dyon states. This construction yields the correct asymptotic states for the scattering of electric and magnetic charges, with pairwise helicity identified as $q_{ij}=e_i{g}_j-e_j{g}_i$.

中文翻译：

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完成庞加莱群的多粒子表示

我们扩展了渐近多粒子状态的定义 $秒$-矩阵超出单粒子状态的张量积。我们确定了称为成对螺旋度的新量子数，或者$q_{\mathrm{一世}j}$，与渐近分离的粒子对相关联。我们首先独立处理所有单个粒子和粒子对，使我们能够概括 Wigner 构造，并最终投影到物理状态。我们的状态减少到张量积状态消失$q_{\mathrm{一世}j}$，而对于消失自旋，它们再现了 Zwanziger 的标量 dyon 状态。这种构造为电荷和磁荷的散射产生了正确的渐近状态，成对的螺旋度被确定为$q_{\mathrm{一世}j}={\mathrm{电子}}_{\mathrm{一世}}{G}_j-{\mathrm{电子}}_j{G}_{\mathrm{一世}}$.