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Analysis of a family of strongly commuting self-adjoint operators with applications to perturbed d'Alembertians and the external field problem in quantum field theory
| Title: | Analysis of a family of strongly commuting self-adjoint operators with applications to perturbed d'Alembertians and the external field problem in quantum field theory |
| Authors: | Arai, A. Browse this author | | Tominaga, N. Browse this author |
| Issue Date: | 1-Feb-1995 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 281 |
| Start Page: | 2 |
| End Page: | 44 |
| Abstract: | A family of strongly commuting self-adjoint operators associated with some objects in the d-dimensional Minkowski space is introduced and operator calculi concerning these self-adjoint operators and the canonical momentum operator p = (p0, PI, …, Pd-I) are developed. It is shown that a class of unitary transformations of Pﾂｵ is given by a class of operator-valued Lorentz transformations of perturbed Pﾂｵ 's. Moreover, the integral kernels of the unitary groups of perturbed d' Alembertians are explicitly computed. As an application, a detailed analysis of the quantum theory of a charged spinless relativistic particle in an external electromagnetic field is given. The present analysis clarifies a genﾂｭeral mathematical structure behind Schwinger's proper-time method for the external field problem in quantum field theory. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69032 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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