2003 Fiscal Year Final Research Report Summary
Mathematical Analysis of a System of a Dirac Particle Interacting With a Quantum Electronagnetid Field
| Project/Area Number |
13440039
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Hokkaido University |
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Principal Investigator |
ARAI Asao Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (80134807)
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| Co-Investigator(Kenkyū-buntansha) |
INOUE Akihiko Hokkaido Univ., Grad.School of Sci., Asso.Prof., 大学院・理学研究科, 助教授 (50168431)
KISHIMOTO Akitaka Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (00128597)
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| Project Period (FY) |
2001 – 2003
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| Keywords | Dirac particle / Dirac operator / Dirac-Maxwell operator / Fock space / Scaling limit / Enhanced binding |
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| Research Abstract |
(i)A Hamiltonian H of a quantum system of a Dirac particle interacting with a quantum electromagnetic field is described by a Dirac-Maxwell operator. The nonrelativistic limit of H is considered. It is proven that a scaled Hamiltonian H_c with a parameter c converges in the strong resolvent sense to the Pauli-Fierz Hamiltonian as c tends to infinity.
(ii)Existence of a scaling limit of H which yields an effective Hamiltonian of the quantum system under consideration.
(iii)Existence of the enhanced binding of a class of quantum systems in nonrelativisitc quantum field theory.
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