Quantum inequalities in integrable models and perturbative gravity in de Sitter space

在这个项目中，学生将开展以下两个主题之一的研究：(1)众所周知，在量子场论中，能量密度可以变为负值。然而，负能量密度有一个下界，称为量子能量不等(QEIs)。量子力学主要建立在线性场论中，但最近也建立了一些自相互作用模型，特别是在可积量子场论中，如大质量伊辛模型。学生将研究这类不等式是否适用于质量伊辛模型中更一般的一类量子可见，而不是能量密度的例子。(2)DS空间中的质量标量场论的QFT已被证明等价于球面上的欧几里德QFT，这比原始的洛伦兹理论更容易分析。然而，DS空间中的其他重要理论，如杨-米尔斯理论和微扰引力理论，是否能在欧几里得球面上得到表述，目前尚不清楚。学生将研究在DS空间中将微扰引力表述为球面上的欧几里得理论的可能性。

In this project the student will carry out research in one of the following two topics:(1) It is well known that the energy density can become negative in quantum field theory. However, there are lower bounds on the negative energy density called quantum energy inequalities (QEIs). QEIs have been established mainly for linear field theories, but recently also for some self-interacting models, notably in integrable quantum field theories such as the massive Ising model. The student will investigate whether inequalities of this kind hold for a more general class of quantum observables in the massive Ising model, beyond the example of the energy density.(2) QFT of massive scalar field theory in dS space has been shown to be equivalent to the Euclidean QFT on the sphere, which is much easier to analyse than the original Lorentzian theory. However, it is not known whether other important theories, such as Yang-Mills theory and perturbative gravity, in dS space can be formulated on the Euclidean sphere. The student will investigate the possibility of formulating perturbative gravity in dS space as a Euclidean theory on the sphere.