Beyer Quantum Spin and Representations of the Poincaré Group, Part I

With a Focus on Physics and Operator Theory
1. Auflage 2025
ISBN: 978-3-031-84140-8
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 227 Seiten

Reihe: Synthesis Lectures on Engineering, Science, and Technology

This book discusses how relativistic quantum field theories must transform under strongly continuous unitary representations of the Poincaré group. The focus is on the construction of the representations that provide the basis for the formulation of current relativistic quantum field theories of scalar fields, the Dirac field, and the electromagnetic field.  Such construction is tied to the use of the methods of operator theory that also provide the basis for the formulation of quantum mechanics, up to the interpretation of the measurement process.  In addition, since representation spaces of primary interest in quantum theory are infinite dimensional, the use of these methods is essential. Consequently, the book also calculates the generators of relevant strongly continuous one-parameter groups that are associated with the representations and, where appropriate, the corresponding spectrum.  Part I of specificallyaddresses: conventions; basic properties of SO(2) and SO(3); construction of a double cover of SO(3); SU(2) spinors; continuous unitary representation of SU(2); basic properties of the Lorentz Group; unitary representation of the restricted Lorentz Group; an extension to a strongly continuous representation of the restricted Poincaré Group; and an extension to a unitary/anti-unitary representation of the Poincaré Group.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Beyer, Horst R.

Inhaltsverzeichnis

Introduction.- Conventions.- Prerequisites.- Basic Properties of SO(2).- Basic Properties of SO(3).- Construction of a Double Cover of SO(3).- SU(2)-Spinors.- A Strongly Continuous Unitary Representation of SU(2).- Basic Properties of the Lorentz Group.- Unitary Representation of the Restricted Lorentz Group.- An Extension to a Strongly Continuous Representation of the Restricted Poincaré Group.- An Extension to a Unitary/Anti-unitary Representation of the Poincaré Group.-Appendix.- Bibliography.- Index of Symbols.- Index.

Über Autor(innen)

Horst R. Beyer, Ph.D., is currently affiliated with the University of Tuebingen Institute for Astronomy and Astrophysics, Theoretical Astrophysics Division. Dr. Beyer has written 8 books and 39 published articles. His research interests include mathematical physics, in particular the applications of operator theory in quantum field theory, general relativity, astrophysics, and the engineering sciences.