Groups and Symmetries

From Finite Groups to Lie Groups
2. Auflage 2022
ISBN: 978-3-030-94359-2
Verlag: Springer International Publishing

Buch, Englisch, 251 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 467 g

Reihe: Universitext

- Combines material from many areas of mathematics, including algebra, geometry, and analysis, so students see connections between these areas

- Applies material to physics so students appreciate the applications of abstract mathematics

- Assumes only linear algebra and calculus, making an advanced subject accessible to undergraduates

- Includes 142 exercises, many with hints or complete solutions, so text may be used in the classroom or for self study

Zielgruppe

Graduate

Autoren/Hrsg.

Kosmann-Schwarzbach, Yvette

Weitere Mitwirkende

Singer, Stephanie Frank

Fachgebiete

• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Quantenphysik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Introduction.- 1. General Facts About Groups.- 2. Representations of Finite Groups.- 3. Representations of Compact Groups.- 4. Lie Groups and Lie Algebras.- 5. Lie Groups SU(2) and SO(3).- 6. Representations of SU(2) and SO(3).- 7. Spherical Harmonics.- 8. Representations of SU(3) and Quarks.- 9. Spin Groups and Spinors.- Problems and Solutions.- Endnote.- Bibliography.-Index.

Über Autor(innen)

A former student of the École Normale Supérieure in Paris, Yvette Kosmann-Schwarzbach holds a Doctorat d’État in mathematics as well as a degree in physics from the University of Paris. She has been a professor of mathematics at the University of Lille, at Brooklyn College of the City University of New York, and at the École Polytechnique (France). She has organized numerous conferences, and has held visiting positions and lectured on four continents.

The author of the historical study, The Noether Theorems, Invariance and Conservation Laws in the Twentieth Century (Sources and Studies in the History of Mathematics and Physical Sciences), she has published over 90 research articles in differential geometry, algebra and mathematical physics, and has co-edited The Verdier Memorial Conference on Integrable Systems (Progress in Mathematics), Integrability of Nonlinear Systems (Lecture Notes in Physics) and Discrete Integrable Systems (Lecture Notes in Physics).