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Models of relative and non-relative Coulomb systems. (Modelle relativistischer und nicht-relativistischer Coulomb-Systeme.) (English) Zbl 1187.81005

Berlin: Logos Verlag; München: Univ. München, Fakultät für Mathematik, Informatik und Statistik (Diss.) (ISBN 978-3-8325-2054-0/pbk). ix, 155 p. (2008).
In his dissertation “Models of relativistic and non-relativistic Coulomb systems” (in German) the author Matthias Huber discusses spectral properties of Dirac operators and uses these to derive lifetime estimates of excited states for realistic systems. Since for many-particle problems Coulomb interactions become relevant, this is a highly challenging task already in the non-relativistic case. Chapter I gives a short review of the literature and summarizes the main result of the thesis. I would have preferred a motivation in this place that addresses a broader audience. For example, abbreviations and technical termini are used in the very first pages in abundance and sometimes even without definition. Part 1 consists of two chapters on self-adjoint Dirac operators and complex dilated Dirac operators and continues the style of chapter I. The motivation for chapter III is significantly too short to interest a non-specialist in this field. Part 2 contains a single chapter IV and provides a better motivation for its content, the energy minimization via the Dirac-Fock functional. Part 3 addresses physical problems: The interaction of few-electron atoms with a radiation field. The first chapter of this part considers a non-relativistic description of electrons, which is finally applied to the hydrogen atom. The second chapter provides the relativistic treatment, which however yields to lowest order in the fine structure constant the same results as the non-relativistic treatment.
Reviewer’s remark: Generally, it can be remarked that some formulations are not just favourable for publication as a book. Non-specialists will miss explanations of technical termini as well as more careful descriptions of figures to access the value of the results illustrated. Clearly, there are many interesting features and results distributed in the text that a specialist may read with profit.

MSC:

81-02 Research exposition (monographs, survey articles) pertaining to quantum theory
83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
81V10 Electromagnetic interaction; quantum electrodynamics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81S99 General quantum mechanics and problems of quantization
81T99 Quantum field theory; related classical field theories
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