论文标题
量子场理论的驯服性，第一部分 - 振幅
The Tameness of Quantum Field Theory, Part I -- Amplitudes
论文作者
论文摘要
就数学逻辑中的驯服概念而言，我们为物理理论提出了一般性的有限原则。驯服的功能或空间只能在我们解释的确切意义上具有有限的结构。驯服性将分析函数的概念推广到包括某些非分析限制，我们表明这包括许多在物理学中出现的限制。对于可重新分配的量子场理论，我们提供了一个一般证据，表明环路扩展中每个顺序的幅度是外部动量和耦合的驯服函数。然后，我们考虑各种确切的非扰动结果，并表明它们是驯服的，但仅对理论的紫外线定义受到限制。这为第二作者最近的猜想提供了进一步的证据，表明所有可以耦合到量子重力的有效理论都是驯服的。我们还讨论了重新归一化组的流量是否为驯服，并评论结果对有效理论的适用性。
We propose a generalized finiteness principle for physical theories, in terms of the concept of tameness in mathematical logic. A tame function or space can only have a finite amount of structure, in a precise sense which we explain. Tameness generalizes the notion of an analytic function to include certain non-analytic limits, and we show that this includes many limits which are known to arise in physics. For renormalizable quantum field theories, we give a general proof that amplitudes at each order in the loop expansion are tame functions of the external momenta and the couplings. We then consider a variety of exact non-perturbative results and show that they are tame but only given constraints on the UV definition of the theory. This provides further evidence for the recent conjecture of the second author that all effective theories that can be coupled to quantum gravity are tame. We also discuss whether renormalization group flow is tame, and comment on the applicability of our results to effective theories.
