Studies of the mathematical properties of Regge-pole and dual amplitudes are important both for their applications in high energy phenomenology and in their generalizations to strings, superstrings, branes, and other theoretical developments. In this paper, we investigate the similarities and differences between two classes of dual amplitudes: one with Mandelstam analyticity (DAMA) and another one with logarithmic trajectories (Dual-log). By using quantum (q-) deformations, new features of Dual-log amplitude are unveiled, in particular those concerning its asymptotic behavior and the spectrum of resonances. The two classes of dual amplitudes are compared in various kinematic regions: at fixed transferred momenta asymptotic, fixed angle asymptotic, and in the resonance region.

中文翻译：

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面对强相互作用的双重模型

研究雷格极点和双振幅的数学特性对于它们在高能现象学中的应用以及它们对弦、超弦、膜和其他理论发展的推广都很重要。在本文中，我们研究了两类双振幅之间的异同：一类具有 Mandelstam 分析 (DAMA)，另一类具有对数轨迹 (Dual-log)。通过使用量子（q-）变形，揭示了双对数振幅的新特征，特别是关于其渐近行为和共振谱的特征。在不同的运动学区域中比较了两类双振幅：在固定传递动量渐近、固定角度渐近和共振区域。