具有次临界紫外奇点的极化子模型的哈密顿量
Hamiltonians for polaron models with subcritical ultraviolet singularities
AI总结：
针对非相对论量子场论中极化子类模型的紫外问题，研究覆盖所有次临界超可重整相互作用，通过有限迭代得到显式自伴的无截断哈密顿量，且截断哈密顿量经基态能量微扰近似扣除后在强预解式意义下收敛于该算子。
摘要：
我们研究了非相对论量子场论中极化子类模型的紫外问题。假设粒子与场的色散关系在无穷远处具有相同的增长性，我们覆盖了所有次临界（超可重整）相互作用。无截断的哈密顿量被表示为通过有限迭代过程得到的显式自伴算子。在减去基态能量的微扰近似后，截断哈密顿量在强预解式意义下收敛于该算子。
英文摘要：
We treat the ultraviolet problem for polaron-type models in nonrelativistic quantum field theory. Assuming that the dispersion relations of particles and the field have the same growth at infinity, we cover all subcritical (superrenormalisable) interactions. The Hamiltonian without cutoff is exhibited as an explicit self-adjoint operator obtained by a finite iteration procedure. The cutoff Hamiltonians converge to this operator in the strong resolvent sense after subtraction of a perturbative approximation for the ground-state energy.
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