Which problems do arise within relativistic enhancements of the Schrödinger theory, especially if one adheres to the usual one-particle interpretation, and to what extent can these problems be overcome? And what is the physical necessity of quantum field theories? In many books, answers to these fundamental questions are given highly insufficiently by treating the relativistic quantum mechanical one-particle concept very superficially and instead introducing field quantization as soon as possible. By contrast, this monograph emphasizes relativistic quantum mechanics in the narrow sense: it extensively discusses relativistic one-particle concepts and reveals their problems and limitations, therefore motivating the necessity of quantized fields in a physically comprehensible way. The first chapters contain a detailed presentation and comparison of the Klein-Gordon and Dirac theory, always in view of the non-relativistic theory. In the third chapter, we consider relativistic scattering processes and develop the Feynman rules from propagator techniques. This is where the impossibility to get around a quantum field theoretical reasoning is discussed and basic quantum field theoretical concepts are introduced. This book addresses undergraduate and graduate physics students who are interested in a clearly arranged and structured presentation of relativistic quantum mechanics in the "narrow sense" and its connection to quantum field theories. Each section contains a short summary and exercises with solutions. A mathematical appendix rounds up this excellent introductory book on relativistic quantum mechanics.
Relativistic Quantum Mechanics Theoretical and Mathematical Physics The series founded in 1975 and formerly (until 2005) entitled Texts and Monographs in Physics (TMP) publishes high-level monographs in theoretical and mathematical physics. The change of title to Theoretical and Mathematical Physics (TMP) signals that the series is a suitable publication platform for both the mathematical and the theoretical physicist. The wider scope of the series is reflected by the composition of the editorial board, comprising both physicists and mathematicians. The books, written in a didactic style and containing a certain amount of elementary background material, bridge the gap between advanced textbooks and research monographs. They can thus serve as basis for advanced studies, not only for lectures and seminars at graduate level, but also for scientists entering a field of research. Editorial Board W. Beiglboeck, Institute of Applied Mathematics, University of Heidelberg, Germany P. Chrusciel, Hertford College, Oxford University, UK J.-P. Eckmann, Université de Genève, Département de Physique Théorique, Switzerland H. Grosse, Institute of Theoretical Physics, University of Vienna, Austria A. Kupiainen, Department of Mathematics, University of Helsinki, Finland M. Loss, School of Mathematics, Georgia Institute of Technology, Atlanta, USA H. Löwen, Institute of Theoretical Physics, Heinrich-Heine-University of Duesseldorf, Germany N. Nekrasov, IHÉS, France M. Salmhofer, Institute of Theoretical Physics, University of Heidelberg, Germany S. Smirnov, Mathematics Section, University of Geneva, Switzerland L. Takhtajan, Department of Mathematics, Stony Brook University, USA J. Yngvason, Institute of Theoretical Physics, University of Vienna, Austria For further volumes: http://www.springer.com/series/720 Armin Wachter Relativistic Quantum Mechanics 13 Dr. Armin Wachter
[email protected] ISSN 1864-5879 e-ISSN 1864-5887 ISBN 978-90-481-3644-5 e-ISBN 978-90-481-3645-2 DOI 10.1007/978-90-481-3645-2 Library of Congress Con