向量丛中的不变随机场及其在宇宙学中的应用
Invariant random fields in vector bundles and application to cosmology
摘要：
我们发展了向量丛中的不变随机场理论。得到了紧致连通李群$G$的诱导表示所生成的齐次向量丛中不变随机场的谱分解。本文讨论了宇宙微波背景理论的一个应用，其中$G=SO(3)$。证明了宇宙学理论中两组不同假设的等价性定理。
英文摘要：
We develop the theory of invariant random fields in vector bundles. The spectral decomposition of an invariant random field in a homogeneous vector bundle generated by an induced representation of a compact connected Lie group $G$ is obtained. We discuss an application to the theory of cosmic microwave background, where $G=SO(3)$. A theorem about equivalence of two different groups of assumptions in cosmological theories is proved.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
