This book is intended as a pedagogical introduction to the subject of the classical and quantum dynamics of gauge fields. It should be accessible to senior undergraduate and beginning graduate students in physics. It assumes that the reader has some background in elementary quantum mechanics and it develops the idea of gauge symmetry from an elementary point of view. The geometrical interpretation of gauge fields is discussed. The formulation of Yang-Mills theory as both a classical and a quantum dynamical system are discussed. Topics of perturbation theory, asymptotic freedom, quark confinement and large N expansions are covered.

Gauge symmetry is at the heart of modern particle physics.  It also makes some interesting appearances in condensed matter physics, particularly in the modeling of strongly correlated electrons.  In teaching courses in physics both at the undergraduate and graduate level, I have come to the realization that it would be a great advantage to the student to master the concepts of gauge invariance and gauge fields earlier than at the graduate level, which is now standard. For this reason, I have set out to put together this book.  It is intended to be a basic introduction to the ideas and some of the structure of gauge field theories.  I have attempted, as much as possible, to make it accessible to the physics student who has a basic familiarity with the standard undergraduate physics curriculum, elementary differential equations, classical mechanics, electricity and magnetism, quantum mechanics and the special theory of relativity. This is typical of senior undergraduate physics majors in North American universities.  At least the first chapter should be easily readable to such a student.  The later chapters which deal with gauge theories as quantum field theories are unavoidably more involved - no matter how you look at it, quantum field theory is a technical subject. Nevertheless, at each opportunity, I have attempted to keep the arguments as simple as possible with the hope that they are understandable to the novice reader.

Gordon Walter Semenoff
University of British Columbia