Collaborative Research: Quantum Vacuum Energy

合作研究：量子真空能

• 批准号: 0554849
• 负责人: Stephen Fulling
• 金额: $ 27.07万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-15 至 2010-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0554849&HistoricalAwards=false
• 关键词: Collaborative; Research; Quantum; Vacuum; Energy

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.

该提案旨在从量子场论的角度研究真空卡西米尔能量及其与谱理论和微分算子渐近性质的联系。数学家和物理学家作为 PI 参与其中。他们建议研究局部和全局重正化真空能量与真空能量符号之间的一致性问题。将特别通过观察特征值能量分布来分析真空能量和周期性经典轨道之间通过半经典马斯洛夫指数的联系。 PI 还建议计算边界边缘和角落附近的真空能量和谱密度：这种奇异边界的谱效应在与广义指数定理相关时也具有数学意义，其中可能包括其他显式物理应用。该项目更广泛的影响部分源于其跨学科性质。真空能与新的纳米技术设备和宇宙学问题（“暗能量”）相关。从数学上讲，周期轨道理论与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。将招募物理和数学领域的本科生和研究生研究助理。