AI 中文总结
本研究证明玻色二次哈密顿量基态与能量随耦合常数变化的全纯性，为微扰展开提供严格依据，还确定了两类模型的收敛半径，验证Pauli-Fierz模型微扰在物理电荷处收敛。
AI 中文摘要
我们研究玻色二次哈密顿量的基态及其能量相对于耦合常数的全纯性，证明了确立该全纯性的一般性定理，从而为形式微扰展开提供严格的数学依据。该理论被应用于多个具体模型，包括单对相互作用模型与偶极近似下的Pauli-Fierz模型。重要的是，对于具有现实紫外截断的Pauli-Fierz模型，即使考虑质量重整化，以基本电荷为参数的微扰展开在物理电荷值处仍收敛。此外，我们明确确定了单对相互作用模型以及平移不变Pauli-Fierz模型的纤维对应的基态及其能量的收敛半径。
英文摘要
We study the holomorphy of the ground state and its energy with respect to the coupling constant for bosonic quadratic Hamiltonians. We prove general theorems establishing this holomorphy, thereby providing a rigorous justification for formal perturbative expansions. This theory is applied to several concrete models, including the single pair interaction model and the Pauli-Fierz model in the dipole approximation. Importantly, for the Pauli-Fierz model with a realistic ultraviolet cutoff, the perturbation expansions in the elementary charge converge at the physical charge value, even when mass renormalization is taken into account. Furthermore, we explicitly determine the radii of convergence of the ground states and their energies for both the single pair interaction model and the fibers of the translation-invariant Pauli-Fierz model.
Comments57 pages, 3 figures
