洛伦兹流形上Wetterich方程的代数量子场论方法
An algebraic QFT approach to the Wetterich equation on Lorentzian manifolds
AI总结：
本文利用微扰代数量子场论中的局域调节子技术，在通用洛伦兹时空中构造了接近Wetterich方程的流方程，并证明了热态及de Sitter时空Bunch-Davies态下存在非平凡固定点。
摘要：
我们讨论相互作用标量量子场论在具有洛伦兹号差的通用时空上以及处于通用态（包括真空态和热态，如果它们存在的话）时有效作用的标度行为。这是通过构造一个流方程来完成的，该方程与著名的Wetterich方程非常接近，所用技术是最近在微扰代数量子场论（pAQFT）领域中发展起来的方法。使得人们能够在通用洛伦兹背景上获得一个有意义的方程的关键要素是使用一个局域调节子，它保持理论的协变性。作为概念验证，所发展的方法被用来表明，在热态下的量子场论中以及在de Sitter时空上处于Bunch-Davies态的量子场情形中，会出现非平凡的固定点。
英文摘要：
We discuss the scaling of the effective action for the interacting scalar quantum field theory on generic spacetimes with Lorentzian signature and in a generic state (including vacuum and thermal states, if they exist). This is done constructing a flow equation, which is very close to the renown Wetterich equation, by means of techniques recently developed in the realm of perturbative Algebraic Quantum Field theory (pAQFT). The key ingredient that allows one to obtain an equation which is meaningful on generic Lorentzian backgrounds is the use of a local regulator, which keeps the theory covariant. As a proof of concept, the developed methods are used to show that non-trivial fixed points arise in quantum field theories in a thermal state and in the case of quantum fields in the Bunch-Davies state on the de Sitter spacetime.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
