Quantum energy inequalities and their implications in semiclassical gravity

在广义相对论中，能量条件(ECs)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，如质量的正性。ECS在理解时空结构方面起着至关重要的作用。尽管它们被广泛使用，但点式ECs通常并不成立。特别值得一提的是，由于负能态的存在，量子场论违背了经典的点态ECs。量子能量不等式(QEIs)被用来约束负能量的积累。虽然量子力学已被广泛地建立在量子力学中，但自作用理论并没有普遍的结果。我的博士学位的目的是为量子力学在相互作用的量子力学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。在协作工作中，我们将与重力的非最小耦合描述为一种有效场论，其中场值由理论的截止来控制。这使得我们能够证明，在一个时空区域内平均的零能量服从一个与状态有关的界限。此外，我们还研究了$d$维CFT中的零能量。我们探索了在由应力-能量张量对真空的作用所定义的状态类中出现大负零能的可能性。虽然负能量是可能的，但对于基于大N因式分解的分析，我们还没有找到中心电荷量级的零能量。

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.