1st Edition
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.
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
Biography
Girish S. Setlur
