Convergent expansions in non-relativistic QED: Analyticity of the ground state
Convergent expansions in non-relativistic QED: Analyticity of the ground state
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非相对论 QED 中的收敛展开：基态的解析性
DOI：
10.1016/j.jfa.2011.07.023
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
I. Herbst
中科院分区：
文献类型：
--
作者：
D. Hasler;I. Herbst
我们在非相对论qed框架下考虑原子的基态。我们表明，基态以及基态能量的解析函数的耦合常数耦合到矢量势，假设原子的哈密顿量有一个非简并的基态。此外，我们表明，相应的展开系数正是相关的雷利-薛定谔级数的系数。作为推论，我们得到在紫外截止为Rydberg能量量级的标度极限下，基态和基态能量对精细结构常数α具有收敛的幂级数展开式，且与α相关的系数对α ≠ 0是有限的.
We consider the ground state of an atom in the framework of non-relativistic qed. We show that the ground state as well as the ground state energy are analytic functions of the coupling constant which couples to the vector potential, under the assumption that the atomic Hamiltonian has a non-degenerate ground state. Moreover, we show that the corresponding expansion coefficients are precisely the coefficients of the associated Raleigh–Schrödinger series. As a corollary we obtain that in a scaling limit where the ultraviolet cutoff is of the order of the Rydberg energy the ground state and the ground state energy have convergent power series expansions in the fine structure constant α, with α dependent coefficients which are finite for α⩾0.