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

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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.