向量值空间上发展方程的规范理论
Towards a gauge theory for evolution equations on vector-valued spaces
摘要：
研究了向量值扩散方程和薛定谔方程的对称性。对于可分希尔伯特空间$H$，我们刻画了$L^2(Ω, H)$的局部子空间（即，定义的逐点），并讨论了微分方程的时间演化下的不变性问题。在这种情况下，我们的结果和规范对称性理论在数学物理之间的连接的可能性进行了探讨。
英文摘要：
We investigate symmetry properties of vector-valued diffusion and Schrödinger equations. For a separable Hilbert space $H$ we characterize the subspaces of $L^2(Ω, H)$ that are local (i.e., defined pointwise) and discuss the issue of their invariance under the time evolution of the differential equation. In this context, the possibility of a connection between our results and the theory of gauge symmetries in mathematical physics is explored.
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