This book is a concise introduction to the key concepts of classical field theory for beginning graduate students and advanced undergraduate students who wish to study the unifying structures and physical insights provided by classical field theory without dealing with the additional complication of quantization. In that regard, there are many important aspects of field theory that can be understood without quantizing the fields. These include the action formulation, Galilean and relativistic invariance, traveling and standing waves, spin angular momentum, gauge invariance, subsidiary conditions, fluctuations, spinor and vector fields, conservation laws and symmetries, and the Higgs mechanism, all of which are often treated briefly in a course on quantum field theory.

This volume is intended as a systematic introduction to gauge field theory for advanced undergraduate and graduate students in high energy physics. The discussion is restricted to the classical (non-quantum) theory in Minkowski spacetime. Particular attention has been given to conceptual aspects of field theory, accurate definitions of basic physical notions, and thorough analysis of exact solutions to the equations of motion for interacting systems.

The author uses a unique approach which emphasizes the field theoretic aspects of gravitation and the strong analogies between gravitation and the other areas that are studied in physics. The theory-centered text begins with the simplest experimental facts then proceeds to the corresponding differential equations, theoretical constructs such as energy, momentum and stress and several applications. End-of-chapter problems provide students with an opportunity to test their understanding, serve as an introduction to and a review of material not included in the book and can be used to develop examples, extensions and generalizations of the material presented.

An introduction to classical field theory focusing on methods and solutions, providing a foundation for the study of quantum field theory.

Dynamics of Classical and Quantum Fields: An Introduction focuses on dynamical fields in non-relativistic physics. Written by a physicist for physicists, the book is designed to help readers develop analytical skills related to classical and quantum fields at the non-relativistic level, and think about the concepts and theory through numerous problems. In-depth yet accessible, the book presents new and conventional topics in a self-contained manner that beginners would find useful. A partial list of topics covered includes: Geometrical meaning of Legendre transformation in classical mechanics Dynamical symmetries in the context of Noether’s theorem The derivation of the stress energy tensor of the electromagnetic field, the expression for strain energy in elastic bodies, and the Navier Stokes equation Concepts of right and left movers in case of a Fermi gas explained Functional integration is interpreted as a limit of a sequence of ordinary integrations Path integrals for one and two quantum particles and for a fermion in presence of a filled Fermi sea Fermion and boson Fock spaces, along with operators that create and annihilate particles Coherent state path integrals Many-body topics such as Schrieffer Wolff transformation, Matsubara, and Keldysh Green functions Geometrical meaning of the vortex-vortex correlation function in a charged boson fluid Nonlocal particle-hole creation operators which diagonalize interacting many-body systems The equal mix of novel and traditional topics, use of fresh examples to illustrate conventional concepts, and large number of worked examples make this book ideal for an intensive one-semester course for beginning Ph.D. students. It is also a challenging and thought provoking book for motivated advanced undergraduates.

Special relativity -- Point particle fields -- Field Lagrangians -- Gravity