Resonances of Dirac operators

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540176
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Ehime University
• Principal Investigator: ITO Hiroshi 愛媛大学, 理工学研究科, 教授 (90243005)
• Co-Investigator(Renkei-kenkyūsha): YAMADA Osanobu 立命館大学, 理工学部, 教授 (70066744) ; TAMURA Hideo 岡山大学, 理学部, 教授 (30022734) ; NOMURA Yuji 愛媛大学, 理工学研究科, 准教授 (40282818) ; IWATSUKA Akira 京都工芸繊維大学, 工芸科学研究科, 教授 (40184890)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: ディラック作用素 / パウリ作用素 / スペクトル / レゾナンス / 非相対論的極限 / シュレーディンガー作用素

Outline of Final Research Achievements

We study the spectral properties of the Dirac operator, appeared in the relativistic quantum mechanics, with a bounded magnetic potential and an unbounded electric potential. These potentials are assumed to be analytic in some sense. We first determine the structure of the spectrum of the Dirac operator. Then, we show that if the speed of light is sufficiently large the Dirac operator has resonances (complex eigenvalues) near eingenvalues and resonances of two Pauli operators appeared in the nonrelativistic quantum mechanics.

Free Research Field

量子力学におけるスペクトル理論および数学的散乱理論