Costa G., Fogli G. Symmetries and Group Theory in Particle Physics. An Introduction to Space-Time and Internal Symmetries

Springer-Verlag Berlin Heidelberg, 2012. — 291 p. — (Lecture Notes in Physics 823). — ISBN: 978-3-642-15482-9 (eBook), 978-3-642-15481-2 (Softcover).Symmetries, coupled with the mathematical concept of group theory, are an essential conceptual backbone in the formulation of quantum field theories capable of describing the world of elementary particles. This primer is an introduction to and survey of the underlying concepts and structures needed in order to understand and handle these powerful tools. Specifically, in Part I of the book the symmetries and related group theoretical structures of the Minkowskian space-time manifold are analyzed, while Part II examines the internal symmetries and their related unitary groups, where the interactions between fundamental particles are encoded as we know them from the present standard model of particle physics.This book, based on several courses given by the authors,addresses advanced graduate students and non-specialist researcherswishing to enter active research in the field, and having a working knowledge of classical field theory and relativistic quantum mechanics. Numerous end-of-chapter problems and their solutions will facilitate the use of this book as self-study guide or as course book for topical lectures.Introduction to Lie Groups and Their Representations.
The Rotation Group.
The Homogeneous Lorentz Group.
The Poincaré Transformations.
One Particle and Two Particle States.
Discrete Operations.
Relativistic Equations.
Unitary Symmetries.
Gauge Symmetries.