Dynamics of Classical and Quantum Fields : An Introduction

This text focuses on non-relativistic physics applicable to low-energy situations. Taking a problem-oriented approach, the author develops the theory with the goal of enabling students to formulate and solve problems of their own. Students are encouraged to think about the concepts and theory through numerous problems, helping them develop analytical skills related to classical and quantum fields at the non-relativistic level. In an in-depth yet accessible way, the author presents many topics that would otherwise be intimidating to beginners, such as "second" quantization path integrals.

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.