Research on Operator Analysis for Nonrelativistic Quantum Dynamics in High Energy Region

在非相对论量子电动力学中存在一些数学问题。特别是，我们一直关注高能区的紫外线突变，以及去除紫外线截止点后的红外突变。Hirokawa在数学上建立了一些关于紫外线突变和/或红外突变的问题。广岛和Spohn研究了电子的重整化质量。广川、广岛和Spohn已经成功地消除了所谓的Nelson模型的紫外线和红外截止，Nelson模型描述了电子与光子在类氢原子中的耦合。此外，Hirokawa澄清说，在与Hainzl和Spohn合作去除这两个截止点后，正则微扰理论的结果仍然适用于上述模型。他们用非微扰方法证明了这一点。广川与田村研究了散射理论，与田中研究了紫外线灾变的奇异性问题，与佐藤研究了基态的唯一性。

There are some mathematical problems in nonrelativistic quantum electrodynamics. Especially, we have been concerned with ultraviolet catastrophe in high energy region and moreover infrared catastrophe after removing ultraviolet cutoff.Hirokawa established some problems on ultraviolet catastrophe and/or infrared castastrophe in mathematics. Hiroshima and Spohn investigated the renormalized mass of electron. Hirokawa, Hiroshima, and Spohn have succeeded in removing both, ultraviolet and infrared cutoffs for the so-called Nelson model, which describes the electron coupled with photons in such as hydrogen-like atom. Also, Hirokawa clarified that the result by the regular perturbation theory is still available in the above model after removing both cutoffs in collaboration with Hainzl and Spohn. They employed a nonperturbative method to prove it.Hirokawa studied scattering theory with Tamura, problem on singularity of ultraviolet catastrophe with Tanaka, and uniqueness of the ground state with Sato.