论文标题
固定kaluza-klein空间上的痕量公式
A Trace Formula on Stationary Kaluza-Klein Spacetimes
论文作者
论文摘要
我们证明了V. guillemin和A. Uribe的梯子渐近学的相对论版本[差异几何学杂志，32（2）：315-347，1990]在全球双重，固定，固定的，空间紧凑的空间上配备了Kaluza-Klein-klein-klein glein Metric的主捆绑包上。这涉及了解当结构组的不可约定表示的同种型子空间时，在kaluza-klein时空上的波方程的频谱分布，以使表示的重量接近Weyl腔室中的无限性。这是对A. Strohmaier和S. Zelditch的结果的直接概括[Indagationes Mathematicae 32（2021），323-363]，并且与Strohmaier-Zelditch [数学的进步，第376、2021、107434]和O. Islam Arxiv：2109.09219。此外，我们还展示了如何将这些结果应用于向量束上巨大的klein-gordon方程的频率渐近学，因为一个人将其定义为无限限的表示。
We prove relativistic versions of the ladder asymptotics from V. Guillemin and A. Uribe [Journal of Differential Geometry, 32(2):315-347, 1990] on principal bundles over globally hyperbolic, stationary, spatially compact spacetimes equipped with a Kaluza-Klein metric. This involves understanding the distribution of the frequency spectrum for the wave equation on a Kaluza-Klein spacetime when restricted to the isotypic subspace of an irreducible representation of the structure group, in the limit that the weight of the representation approaches infinity in the Weyl chamber. This is a direct generalization of the results from A. Strohmaier and S. Zelditch [Indagationes Mathematicae 32 (2021), 323-363] and is closely related to Strohmaier-Zelditch [Advances in Mathematics, Volume 376, 2021, 107434] and O. Islam arXiv:2109.09219. Furthermore we show how to apply these results to frequency asymptotics for the massive Klein-Gordon equation on vector bundles as one takes the representation defining the vector bundle to infinity.
