Groups, Matrices, and Vector Spaces: A Group Theoretic Approach to Linear Algebra

1. Preliminaries.- 2. Groups and Fields: The Two Fundamental Notions of Algebra.- 3. Vector Spaces.- 4. Linear Mappings.- 5. Eigentheory.- 6. Unitary Diagonalization and Quadratic Forms.- 7. The Structure Theory of Linear Mappings.- 8. Theorems on Group Theory.- 9. Linear Algebraic Groups: An Introduction.- Bibliography.- Index.

The book is a self-contained introduction to perturbative and nonperturbative Quantum chromodynamics (QCD) with worked-out exercises for students of theoretical physics. It will be useful as a reference for research scientists as well. Starting with the hadron spectrum, the reader becomes familiar with the representations of SU(N). Relativistic quantum field theory is recapitulated, and scattering theory is discussed in the framework of scalar quantum electrodynamics. Then the gauge theory of quarks and gluons is introduced. In the more advanced chapters, perturbative and nonperturbative techniques in state-of-the-art QCD are discussed in great detail.
The new third edition has been extensively revised and enlarged to cover all new aspects in Quantum chromodynamics.