Dynamics of Classical and Quantum Fields: An Introduction, 1st Edition (Hardback) book cover

Dynamics of Classical and Quantum Fields

An Introduction, 1st Edition

By Girish S. Setlur

CRC Press

370 pages | 64 B/W Illus.

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Description

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.

Table of Contents

The Countable and the Uncountable

Review of Lagrangian Mechanics

The Hamiltonian Formulation

Flows and Symmetries

Dynamics of a Continuous System

Variational Methods

Symmetries and Noether’s Theorem

Noether’s Theorem in a Lagrangian Setting

Noether’s Theorem in a Hamiltonian Setting

Dynamical Symmetries

Symmetries in Field Theories

The Electromagnetic Field and Stress Energy Tensor

Relativistic Nature of the Electromagnetic Field

Lagrangian of the EM Field

Stress Energy Tensor of the EM Field

Solution of Maxwell’s Equations Using Green’s Functions

Diffraction Theory

Elasticity Theory and Fluid Mechanics

Stress and Strain Tensor of Deformable Bodies

Strain Energy

Euler and Navier Stokes Equations

Bernoulli’s equation for an incompressible fluid

Navier Stokes Equation

Conserved Quantities and Dissipation Rates

Turbulence

Toward Quantum Fields: Scalar and Spinor Fields

Some Solutions of the Schrodinger Equation

Some Properties of the Dirac Equation and Klein Gordon Equations

Concept of functional integration

Integration over Functions

Perturbation Theory

Quantum Mechanics Using Lagrangians: Path Integrals

The Formalism

Free Particles

Harmonic Oscillator

Two-Particle Green Functions

Creation and Annihilation Operators in Fock Space

Introduction to Second Quantization

Creation and Annihilation Operators in Many-Body Physics

Green Functions in Many-Body Physics

Hamiltonians Using Creation and Annihilation Operators

Current Algebra

Quantum Fields on a Lattice

Derivation of the Tight Binding Picture

Schrieffer-Wolff Transformation

Green Functions: Matsubara and Nonequilibrium

Matsubara Green Functions

Nonequilibrium Green Functions

Schwinger-Dyson Equations

Coherent State Path Integrals

CSPI for a Harmonic Oscillator

CSPI for a Fermionic Oscillator

Generalization to Fields

Nonlocal Operators

Quantum Vortices in a Charged Boson Fluid

Nonlocal Particle Hole Creation Operators

The Sea-Boson

Non-chiral Bosonization of Fermions in One Dimension

A Critique of Conventional Chiral Bosonization

General Considerations

Impurity in a Luttinger Liquid

Closed Form for Full Propagator

Subject Categories

BISAC Subject Codes/Headings:
SCI055000
SCIENCE / Physics
SCI057000
SCIENCE / Quantum Theory
SCI077000
SCIENCE / Solid State Physics