Collaborative Research: Quantum Vacuum Energy

从量子场论的角度研究真空Casimir能量及其与谱理论和微分算符的渐近性质的关系。数学家和物理学家作为PI参与其中。他们建议研究局域和全局重整化真空能量以及真空能量符号之间的一致性问题。通过半经典Maslov指数分析真空能量和周期经典轨道之间的联系，特别是通过观察本征值能量分布。PI还建议计算边界边缘和边角附近的真空能量和谱密度：这种奇异边界的谱效应也是与广义折射率定理有关的数学兴趣，这可能包括其他显式的物理应用。该项目的广泛影响在一定程度上源于其跨学科性质。真空能源既与新的纳米技术设备有关，也与宇宙学问题(“暗能量”)有关。在数学上，周期轨道理论和真空能量之间的联系以及真空能量对光谱理论的影响几乎没有被探索过。将招聘来自物理和数学的本科生和研究生研究助理。

The proposal is to investigate the vacuum Casimir energy from a quantum field theory point of view and its connections to spectral theory and asymptotic properties of differential operators. Mathematicians and physicists are involved as PIs. They propose to work on questions about the consistency between local and global renormalized vacuum energies and the sign of the vacuum energy. The connection between the vacuum energy and periodic classical orbits via the semiclassical Maslov indices will be analyzed in particular by looking at the eigenvalue energy distributions. The PIs propose also to calculate the vacuum energies and spectral densities near boundary edges and corners: the spectral effects of such singular boundaries are also of mathematical interest in connection with generalized index theorems, which may include other explicit physical applications. The broader impact of the project stems partly from its interdisciplinary nature. Vacuum energy is relevant both to new nanotechnology devices and to cosmological issues ("dark energy"). Mathematically, the connection between periodic-orbit theory and vacuum energy and the implications of vacuum energy for spectral theory have barely been explored. Undergraduate and graduate student research assistants from both physics and mathematics will be recruited.