Spectral analysis of quantum field theory on curved space time and its application

分析了弯曲时空中粒子系统的光谱特性。特别地，将去中心化空间视为图，研究了多粒子系统的谱与粒子运动的图的结构之间的关系。证明了粒子哈密顿量的零特征空间和Witten指数在图变换下是不变的。在与上面相同的图形变换下，光谱间隙仍然是开放的。

The spectral properties of particle systems on curved spacetime were analyzed. Particularly, descretized spaces are viewed as graphs, and the relation between the spectra of many-particle systems and the structure of graphs where the particles move was studied. The zero eigenspace and the Witten index of the particle Hamiltonians were proved to be invariant under a graph transformation. The spectral gap was shown to remain open under the same graph transfomation as above.