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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

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/83428

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
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

Submitter: 数学紀要登録作業用

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