高能弦散射振幅与无符号Stirling数恒等式
High-Energy String Scattering Amplitudes and Signless Stirling Number Identity
摘要：
本文给出了最近由高能弦散射振幅的计算提出的一组恒等式（7）的完整证明。这些身份允许一个提取的比率之间的高能量弦散射振幅在固定角度制度从高能量振幅在Regge制度。证明是基于组合理论中的无符号Stirling数恒等式。这些结果对任意实值$L$都是有效的，而不是仅对先前证明的$L=0,1$有效.非整数实值$L$的恒等式最近被证明可以在高能紧致弦散射振幅中实现[He S.，李JC，杨Y，arXiv：1012.3158]。参数$L$与激发弦态的质量水平有关，并且对于卡鲁扎-克莱因模式可以取非整数值。
英文摘要：
We give a complete proof of a set of identities (7) proposed recently from calculation of high-energy string scattering amplitudes. These identities allow one to extract ratios among high-energy string scattering amplitudes in the fixed angle regime from high-energy amplitudes in the Regge regime. The proof is based on a signless Stirling number identity in combinatorial theory. The results are valid for arbitrary real values $L$ rather than only for $L=0,1$ proved previously. The identities for non-integer real value $L$ were recently shown to be realized in high-energy compactified string scattering amplitudes [He S., Lee J.C., Yang Y., arXiv:1012.3158]. The parameter $L$ is related to the mass level of an excited string state and can take non-integer values for Kaluza-Klein modes.
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