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首页> 外文期刊>Proceedings of the Royal Society. Mathematical, physical and engineering sciences >Twistor theory at fifty: from contour integrals to twistor strings
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Twistor theory at fifty: from contour integrals to twistor strings

机译：Twistor理论在五十：从轮廓积分到捻线串

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摘要

We review aspects of twistor theory, its aims and achievements spanning the last five decades. In the twistor approach, space-time is secondary with events being derived objects that correspond to compact holomorphic curves in a complex threefold-the twistor space. After giving an elementary construction of this space, we demonstrate how solutions to linear and nonlinear equations of mathematical physics-anti-self-duality equations on Yang-Mills or conformal curvature-can be encoded into twistor cohomology. These twistor correspondences yield explicit examples of Yang-Mills and gravitational instantons, which we review. They also underlie the twistor approach to integrability: the solitonic systems arise as symmetry reductions of anti-self-dual (ASD) Yang-Mills equations, and Einstein-Weyl dispersionless systems are reductions of ASD conformal equations. We then review the holomorphic string theories in twistor and ambitwistor spaces, and explain how these theories give rise to remarkable new formulae for the computation of quantum scattering amplitudes. Finally, we discuss the Newtonian limit of twistor theory and its possible role in Penrose's proposal for a role of gravity in quantum collapse of a wave function.
机译：我们审查了Twistor理论的方面，其目标和成就跨越了过去五十年。在Twistor方法中，时空是次要的，事件被导出对应于复杂的三倍 - 扭转器空间中的紧凑型全旋曲线。在提供这种空间的基本结构之后，我们展示了阳磨机或共形曲率的数学物理 - 抗自二元方程的线性和非线性方程的解态和非线性曲率 - 可以编码为扭转同学。这些扭转者对应条件，杨米尔斯和引力算子的明确示例，我们审查。它们还利用了扭转方法的可积分方法：棒子系统作为抗自行式（ASD）阳铣刀方程的对称减少，而Einstein-Weyl分散系统是减少ASD共形方程的降低。然后，我们在Twistor和Ambitwistor空间中审查了全旋弦理论，并解释了这些理论如何产生卓越的新公式，以计算量子散射幅度。最后，我们讨论了Twistor理论的牛顿极限及其在PenRose在波浪功能中的重心作用中的可能作用。

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