简并未微扰态的Gell-Mann和Low公式
Gell-Mann and Low formula for degenerate unperturbed states
摘要：
Gell-Mann和Low切换允许将未扰动的哈密尔顿算子$H_0$的本征态变换为修改的哈密尔顿算子$H_0 + V$的本征态。当初始本征态不退化时，在某些带隙条件下，可以执行这种切换。我们在这里展示了如何将这种方法扩展到未微扰哈密顿量的基态是简并的情况。更准确地说，我们证明了开关过程仍然可以进行时，初始状态是有限秩自伴算子$\cP_0 V \cP_0$的本征态，其中$\cP_0$是一个退化的本征空间的$H_0$的投影。
英文摘要：
The Gell-Mann and Low switching allows to transform eigenstates of an unperturbed Hamiltonian $H_0$ into eigenstates of the modified Hamiltonian $H_0 + V$. This switching can be performed when the initial eigenstate is not degenerate, under some gap conditions with the remainder of the spectrum. We show here how to extend this approach to the case when the ground state of the unperturbed Hamiltonian is degenerate. More precisely, we prove that the switching procedure can still be performed when the initial states are eigenstates of the finite rank self-adjoint operator $\cP_0 V \cP_0$, where $\cP_0$ is the projection onto a degenerate eigenspace of $H_0$.
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