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

Arai, A.; Tominaga, N.

Hokkaido University Preprint Series in Mathematics, 1995, 281, 2-44

Permalink : https://doi.org/10.14943/83428

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DOI	https://doi.org/10.14943/83428
URI	https://hdl.handle.net/2115/69032
タイトル	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
著者	著者名 Arai, A.
著者	著者名 Tominaga, N.
言語	英語
発行日	1995-02-01
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	281
ページ	2-44
抄録	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.
資源タイプ	紀要論文
出版タイプ	Version of Record