AI 中文总结
本文证明任意维数周期薛定谔算子$ -\Delta+V$的Bloch簇在周期性意义下不可约，方法结合全纯延拓、整数平移及解析几何与扰动估计。
AI 中文摘要
设$d\ge1$且$V\in C(\mathbb{T}^d;\mathbb{C})$。我们证明$ -\Delta+V$的Bloch簇在周期性意义下是不可约的。证明结合了谱带函数的全纯延拓与准动量的整数平移。利用解析几何和沿虚轴的扰动估计，我们证明在适当的整数平移后，所有不可约分量都包含相同的全纯谱支。
英文摘要
Let $d\ge1$ and $V\in C(\mathbb{T}^d;\mathbb{C})$. We prove that the Bloch variety of $-Δ+V$ is irreducible modulo periodicity. The proof combines holomorphic continuation of spectral band functions with integer translations of quasimomentum. Using analytic geometry and perturbation estimates along imaginary rays, we show that, after suitable integer translations, all irreducible components contain the same holomorphic spectral branch.
