This article is an introduction to two research programs that are currently very active, the conformal bootstrap and scattering amplitudes. Rather than attempting full surveys, the emphasis is on common ideas and methods shared by these two seemingly very different programs. In both fields, mathematical and physical constraints are placed directly on the physical observables in order to explore the landscape of possible consistent quantum field theories (QFTs). We give explicit examples from both programs: the reader can expect to encounter boiling water, ferromagnets, pion scattering, and emergent symmetries on this journey into the landscape of local relativistic QFTs. The first part is written for a general physics audience. The second part includes further details, including a new on-shell bottom-up reconstruction of the model with the Fubini–Study metric arising from resummation of the n-point interaction terms derived from amplitudes.

The presentation is an extended version of a colloquium given at the Aspen Center for Physics in August 2019.

这篇文章是对目前非常活跃的两个研究项目的介绍，共形自举和散射幅度。重点不是尝试全面调查，而是强调这两个看似非常不同的程序共享的共同想法和方法。在这两个领域中，数学和物理约束都直接放在物理可观测量上，以探索可能的一致量子场论 (QFT) 的前景。我们从两个程序中给出了明确的例子：在进入局部相对论 QFT 的过程中，读者可能会遇到沸水、铁磁体、pion 散射和涌现对称性。第一部分是为一般物理学读者编写的。第二部分包括更多细节，包括新的壳上自下而上的重建具有 Fubini-Study 度量的模型，该度量源自对从振幅导出的n点相互作用项的求和。

该演讲是 2019 年 8 月在阿斯彭物理中心举行的座谈会的扩展版本。