The present book guides through the symmetries in physics: It introduces and discusses important groups and symmetries from atomic and molecular physics, solid-state physics, particle physics and (quantum) field theory. The book is aimed at physics students who are either attending lectures on group and representation theory or wish to delve into group theory and symmetries in physics as part of their bachelor's, master's, or doctoral thesis. Topics covered include finite and continuous groups, Lie algebras and their representations, as well as quantum mechanics, classical and quantized field theories, gauge theories, and conformal field theories. The author combines the mathematical foundations with physical applications in the chapters. Examples, exercises, and intermediate questions help readers to check their understanding.
Preface.- Abbreviations.- Introduction.- Elements of Group Theory.-
Homomorphisms, Subgroups, and Classes.- Finite Groups.- Space-Time
Symmetries.- Point Groups.- Space Groups and Crystals.- Lie Groups.-
Invariant Integration.- Representations of Groups.- Characters and Schur's
Lemma.- Irreducible Representations of Lie Groups.- Theory of Lie Algebras.-
Lie Algebras of Lie Groups.- Root Systems and Cartan Classification.-
Representations of Lie Algebras.- Symmetries in Quantum Mechanics.-
Symmetries in Relativistic QM.- Relativistic Field Theories.- Gauge
Theories.- Conformal Field Theories.- Index.
Andreas Wipf conducted research at the Dublin Institute for Advanced Studies, Los Alamos National Laboratory, Max Planck Institute for Physics, and ETH Zurich. Since 1995, he has been a professor of quantum theory at Friedrich Schiller University in Jena. His main areas of work are quantum field theory, symmetries and symmetry breaking, supersymmetry, and lattice field theories.
