Dynamics of Classical and Quantum Fields: An Introduction

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.