Symmetries and Group Theory in Particle Physics

1. Front Matter

   Pages i-xiii

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2. Introduction to Lie Groups and Their Representations

   • Giovanni Costa, Gianluigi Fogli

   Pages 1-26

3. The Rotation Group

   • Giovanni Costa, Gianluigi Fogli

   Pages 27-41

4. The Homogeneous Lorentz Group

   • Giovanni Costa, Gianluigi Fogli

   Pages 43-60

5. The Poincaré Transformations

   • Giovanni Costa, Gianluigi Fogli

   Pages 61-70

6. One Particle and Two Particle States

   • Giovanni Costa, Gianluigi Fogli

   Pages 71-82

7. Discrete Operations

   • Giovanni Costa, Gianluigi Fogli

   Pages 83-95

8. Relativistic Equations

   • Giovanni Costa, Gianluigi Fogli

   Pages 97-112

9. Unitary Symmetries

   • Giovanni Costa, Gianluigi Fogli

   Pages 113-168

10. Gauge Symmetries

    • Giovanni Costa, Gianluigi Fogli

    Pages 169-212

11. Back Matter

    Pages 213-291

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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 researchers wishing 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.

• Poincaré group and transformations
• homogenous and inhomogenous Lorentz group
• unitary and gauge symmetries in particle physics
• weight diagrams and Young tableaux

From the reviews:

“The aim of this textbook is to introduce students to group-theoretical aspects in particle physics. To achieve this, the authors first give a brief introduction to the structure of Lie groups and algebras. … The main text is supplemented by a few indices with technical details on group theory, as well as a large set of exercises with solutions. … the book is written in a readable and accessible manner. … the collection of exercises makes it a valuable repository for lecturers.” (Axel Maas, Mathematical Reviews, July, 2013)

“The aim of the monograph is two-fold, to give the basic notions and facts from group and group representation theory for particle physics and to give a survey of their applications in relativistic quantum field theory and particle physics. Therefore it should be considered to be a good handbook.” (Boris V. Loginov, Zentralblatt MATH, Vol. 1243, 2012)

• , Dipt. di Fisica, Università di Padova, Padova, Italy

  Giovanni Costa

• Università die Bari, Dipartimento die Fisica, Bari, Italy

  Gianluigi Fogli

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