论文标题
伪造系统对角线化的拓扑障碍
Topological obstructions to the diagonalisation of pseudodifferential systems
论文作者
论文摘要
鉴于在平滑的歧管上具有矩阵伪差异操作员，可以通过平滑的方式选择其主要符号的特征向量，从而对其对角线感兴趣。我们表明，在整个cotangent束甚至单个纤维中，对角化并非总是可能的。我们确定了对角化的全球和地方拓扑障碍，并检查了物理上有意义的例子，表明所有可能的情况都可能发生。
Given a matrix pseudodifferential operator on a smooth manifold, one may be interested in diagonalising it by choosing eigenvectors of its principal symbol in a smooth manner. We show that diagonalisation is not always possible, on the whole cotangent bundle or even in a single fibre. We identify global and local topological obstructions to diagonalisation and examine physically meaningful examples demonstrating that all possible scenarios can occur.
