|
Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Hokkaido University Preprint Series in Mathematics >
Scaling limit of a model of quantum electrodynamics
| Title: | Scaling limit of a model of quantum electrodynamics |
| Authors: | Hiroshima, F. Browse this author |
| Issue Date: | Apr-1993 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 194 |
| Start Page: | 1 |
| End Page: | 53 |
| Abstract: | This article gives a solution to an open problem in the paper: A.Arai; J.Math.Phys.31, 2653(1990). We present an abstract asymptotic theory of families of unitary operators {U(11:)},.>o and self-adjoint operators {H,.},.>o acting in the tensor product of two Hilbert spaces. We prove that H;en (V, 11: ), which represents a scaled total Hamiltonian of a coupled system of a one electron atom and a quantized radiation :field, with parameters O e 1, 11: > 0, and the electron mass renormlized, is unitarily equivalent to an operator fI;en (V, 11:), which can be regarded as a decoupled Hamiltonian. Applying the abstract asymptotic theory and the unitary equivalence, we prove that the resolvent of H;en (v, 11:) strongly converges as 11: -+ oo to an operator which de:fines an effective potential of the electron. We compare the effective potential with that obtained in the paper mentioned above. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/68940 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
|
Submitter: 数学紀要登録作業用
|
