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TWISTED TALES FROM STRING THEORY

机译：扭曲理论的扭曲故事

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The Regge trajectories, upon which string theory is based, behave as rigid rotators rather than vibrating strings. The same relation, between the angular momentum, and the square of the mass, can be found in gravity, the electroweak, and strong interactions. The angle deficit for cosmic strings is shown to be an angle excess that is related to the increase of the circumference of a uniformly rotating disc. Schrodinger's time independent equation with a centrifugal barrier gives an automorphic function that can be constructed as the ratio of its two independent solutions for values of the angular momentum lying outside of their positive, integer values. If the fixed points 0 and ∞ in the z-plane correspond to -i and +i in the ω-plane, then elliptic substitutions tessellate the ω-plane in the form of cresents, while if the fixed points correspond to -1 and +1 in the ω-plane are source and sink, just like the lines of force between positive and negative charges. The unit disc undergoes a stretching by a Lorentz transform. With the inclusion of a third fixed point, the Schwarz-Christoffel mapping of the z-plane onto the triangle functions of Schwarz is the incomplete Euler beta function found by Veneziano for the 4-point scattering amplitude.
机译：弦理论所基于的Regge轨迹表现为刚性旋转器，而不是振动弦。在重力，电弱和强相互作用中可以发现角动量和质量平方之间的相同关系。宇宙弦的角度赤字显示为与均匀旋转圆盘周长的增加有关的角度过剩。带有离心屏障的薛定inger时间独立方程提供了一个自晶函数，该函数可以构造为其两个独立解的比率，以解决角动量的正整数值以外的问题。如果z平面中的固定点0和∞对应于ω平面中的-i和+ i，则椭圆替换以渐进形式细分ω平面，而如果固定点对应于-1和+ ω平面中的1是源极和漏极，就像正电荷和负电荷之间的力线一样。单位圆盘通过洛伦兹变换进行拉伸。加上第三个固定点，z平面到Schwarz三角函数上的Schwarz-Christoffel映射是Veneziano发现的针对4点散射幅度的不完全Euler beta函数。

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