This book presents the classical foundations upon which quantum theories are built as well as the classical properties of field theories used in a wide variety of quantum systems.

This book is an introduction to classical field theory and the mathematics required to formulate and analyze it. The development of the mathematical formalism, previously in an appendix, is integrated into the presentation of the physical concepts. The book develops the core concepts of field theory by applying Newtonian physics to the stretched string, emphasizing the relationship between fields and the observer's coordinate systems and using basic concepts of differential geometry and functional techniques. The text begins with an introduction to modern differential geometry and functional methods. The author uses basic differential geometry, variational techniques, and group theory to derive the Newtonian theory of fluids and the theories of scalar, spinor, vector, and tensor fields. Numerous classical situations are analysed which have direct implications for quantum field theory. The book closes with classical Yang-Mills fields and a brief introduction to classical string theory.

This collection of insights should be invaluable to both the student, instructors, and active researchers since it presents a unified view of field theories without the added complication of quantization.

Mark Swanson received his Ph.D. in physics from the University of Missouri at Columbia in 1976 under the supervision of Justin Huang. After postdoctoral appointments at the University of Alberta and the University of Connecticut he held a faculty appointment at the University of Connecticut at Stamford from 1983 to 2014, during which time he spent six years in university administrative roles. He is the author of 25 research articles and four monographs, with an emphasis on field theory and path integral techniques. He is currently Emeritus Professor of Physics at the University of Connecticut and lives in Monroe, Connecticut.