Quantum energy inequalities and their implications in semiclassical gravity

在广义相对论中，能量条件（energy conditions，EC）是对应力-能量张量施加的限制，以编码对物质的物理合理约束，例如质量的正性。ECs在理解时空结构方面起着关键作用。尽管它们被广泛使用，逐点EC通常并不成立。特别是量子场论（QFT）违反了经典的逐点EC由于负能量状态的存在。量子能量不等式（QEI）已被推导出来，以限制负能量的积累。虽然QEI已经在QFT中广泛建立，但自相互作用理论还没有普遍的结果。我的博士学位的目标是为QEI在相互作用QFT中的发展及其在半经典引力中的应用做出贡献。这份报告总结了我在博士第一年为实现这一目标所做的工作。在合作工作中，我们已经描述了非最小耦合引力作为一个有效的场论，其中的字段值是由理论的截止控制。这使我们能够证明，在一个时空区域上平均的零能量服从一个依赖于状态的束缚。此外，我们还研究了$d$维CFTs的零能量。我们探讨了在由应力-能量张量对真空的作用所定义的状态类中存在大的负零能的可能性。虽然负能量是可能的，但我们还没有找到基于大N因子分解的分析的中心电荷数量级的零能量。

In general relativity, energy conditions (ECs) are restrictions imposed on the stress-energy tensor to encode physically reasonable constraints on matter such as the positivity of mass. ECs play a critical role in understanding the structure of spacetime. Despite their widespread use, pointwise ECs do not generally hold. In particular quantum field theory (QFT) violates classical pointwise ECs due to the existence of negative energy states. Quantum energy inequalities (QEIs) have been derived to constrain the accumulation of negative energy. While QEIs have been broadly established in QFTs, there is no general result for self-interacting theories.The goal of my PhD is to contribute to the development of QEIs in interacting QFTs and their application to semiclassical gravity. This report summarizes my work towards that goal during the first year of my PhD. In collaborative work, we have described non-minimal coupling to gravity as an effective field theory in which the field value is controlled by the theory's cutoff. This allowed us to show that the null energy averaged over a region of spacetime obeys a state dependent bound. Additionally, we have studied null energy in $d$-dimensional CFTs. We explored the possibility of large negative null energy in the class of states defined by the action of the stress-energy tensor on the vacuum. While negative energy is possible, we haven't found null energy of the order of the central charge for an analysis based on the large-N factorization.