1. Physics in Flat Spacetime: Geometric Viewpoint
1.1 Overview
1.2 Foundational Concepts
1.3 Tensor Algebra Without a Coordinate System
1.4 Particle Kinetics and Lorentz Force Without a Reference Frame
1.5 Component Representation of Tensor Algebra
1.6 Particle Kinetics in Index Notation and in a Lorentz Frame
1.7 Orthogonal and Lorentz Transformations of Bases, and Spacetime Diagrams
1.8 Time Travel
1.9 Directional Derivatives, Gradients, Levi-Civita Tensor, Cross Product and Curl
1.10 Nature of Electric and Magnetic Fields; Maxwell's Equations
1.11 Volumes, Integration, and the Gauss and Stokes Theorems
1.12 The Stress-energy Tensor and Conservation of 4-Momentum
I. STATISTICAL PHYSICS
2. Kinetic Theory
2.1 Overview of this Chapter
2.2 Phase Space and Distribution Function
2.3 Other Norrealizations for the Distribution Function
2.4 Thermal Equilibrium
2.5 Number-Flux Vector and Stress-Energy Tensor
2.6 Perfect Fluids and Equations of State
iii
2.7 Evolution of the Distribution Function: Liouville's Theorem, the Vlasov Equation
and the Boltzmann Transport Equation
2.8 Transport Coefficients
iv
3. Statistical Mechanics
3.1 Overview
3.2 Systems, Ensembles, and Distribution Functions
3.3 Liouville's Theorem and the Evolution of the Distribution Function
3.4 Statistical Equilibrium
3.5 The Microcanonical Ensemble and the Ergodic Hypothesis
3.6 Entropy and the Evolution into Statistical Equilibrium
3.7 Statistical Mechanics of an Ideal Monatomic Gas
3.8 Statistical Mechanics in the Presence of Gravity: Galaxies, Black Holes, the
Universe, and Evolution of Structure in the Early Universe
3.9 Entropy and Information [not yet written]
4. Statistical Thermodynamics
4.1 Overview
4.2 Microcanonical Ensemble and the Energy Representation of Thermodynamics
4.3 Canonical Ensemble and the Free-Energy Representation of Thermodynamics
4.4 The Gibbs Representation of Thermodynamics; Phase Transitions and Chemical
Reactions
4.5 Fluctuations of Systems in Statistical Equilibrium
4.6 The Ising Model and Renormalization Group Methods
4.7 Monte Carlo Methods [not yet written]
Random Processes
Note: In 2000-2001 we will expand this chapter and break it into two.
5.1 Overview
5.2 Random Processes and their Probability Distributions
5.3 Correlation Function, Spectral Density, and Ergodicity
5.4 Noise and its Types of Spectra
5.5 Filters, Signal-to-Noise Ratio and Shot Noise
5.6 The Evolution of a System Interacting with a Heat Bath: Fluctuation-Dissipation
Theorem, Fokker-Planck Equation and BrownJan Motion
v
II. OPTICS
6. Geometrical Optics
6.1 Overview
6.2 Waves in a Homogeneous Medium
6.3 Waves in an Inhomogeneous, Time-Varying Medium: The Eikonal Approximation
6.4 Paraxial Optics
6.5 Polarization and the Berry Phase
6.6 Caustics and Catastrophes
Gravitational Lenses
7. Diffraction
7.1 Overview
7.2 Helmholtz-Kirchhoff Integral: diffraction by an aperture; spreading of the wave-
front
7.3 Fraunhofer Diffraction:
telescope
diffraction grating;
Babinet's principle;
Hubble space
7.4 Fresnel Diffraction: lunar occultation of a radio source; circular apertures
7.5 Fourier Optics: coherent illumination; point spread functions; Abb6 theory; phase
contrast microscopy; Gaussian beams
7.6 Diffraction at a Caustic
8. Interference
8.1 Overview
8.2 Coherence: Young's slits; extended source; van Cittert-Zernike theorem; general
formulation of lateral coherence; lateral coherence length; Michelson stellar inter-
ferometer; temporal coherence; Michelson interferometer; degree of coherence
8.3 Radio Telescopes: two-element interferometer; closure phase; angular resolution
8.4 Etalons and Fabry-Perot Interferometers Gravitational Wave Detection:
multiple-beam interferometry; Fabry-Perot interferometer; lasers
8.5 Laser Interferometer Gravitational Wave Detectors
8.6 Intensity Correlation and Photon Statistics
9. Nonlinear Optics
9.1 Overview
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9.2 Lasers: Basic Principles; Types of Pumping and Types of Lasers
9.3 Holography
9.4 Phase-Conjugate Optics
9.5 Wave-Wave Mixing in Nonlinear Crystals: nonlinear dielectric susceptibility;
wave-wave mixing; resonance conditions and growth equations
9.6 Applications of Wave-Wave Mixing:
squeezing
Fequency doubling;
phase conjugation;
III. ELASTICITY
10. Elastostatics
10.1 Overview
10.2 Strain; Expansion, Rotation, and Shear
10.3 Cylindrical and Spherical
of Strain
Coordinates: Connectio Coefficients and Components
10.4 Stress and Elastic Moduli: stress tensor; elastic moduli; energy of deformation;
molecular origin of elastic stress; Young's modulus and Poisson ratio
10.5 Thermoelastic noise in gravitationa-wave detectors
10.6 Bending of Beams
Cantilever Bridges
10.7 Deformation of Plates
Keck Telescope Mirror
10.8 Bifurcation
Mountain Folding
11. Elastodynamics
11.1 Overview
11.2 Conservation Laws
11.3 Basic Equations of Elastodynamics: equation of motion; elastodynamic waves;
longitudinal sound waves; transverse shear waves; energy of elastodynamic waves
11.4 Waves in Rods, Strings and Beams: compression waves; torsion waves; waves on
strings; flexural waves on a beam; buckling
11.5 Body and Surface Waves body waves; edge waves; Green's function for a
homogeneous half space; free oscillations of solid bodies; seismic tomography
11.6 The Relationship of Classical Waves to Quantum Mechanical Excitations
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IV. FLUID DYNAMICS
12. Foundations of Fluid Dynamics
12.1 Overview
12.2 Hydrostatics: Archimedes law; stars and planets; rotating fluids
12.3 Conservation Laws for an Ideal Fluid: mass conservation; momentum conserva-
tion; Euler equation; Bernoulli principle; energy conservation
12.4 Incompressible Flows
12.5 Viscous Flows: decomposition of the velocity gradient into expansion, vorticity,
and shear; Navier-Stokes equation; energy conservation and entropy production;
molecular origin of viscosity; blood flow
13. Vorticity
13.1 Overview
13.2 Vorticity and Circulation: vorticity transport; tornados; Kelvin's theorem; diffu-
sion of vortex lines; sources of vorticity
13.3 Low Reynolds' Number Flow-
Stokes' flow; Nuclear Winter; sedimentation rate
13.4 High Reynolds' Number Flow
Laminar Boundary Layers: separation
13.5 Kelvin-Helmholtz Instability: temporal and spatial growth; excitation of ocean
waves by wind; physical interpretation; the Rayleigh and Richardson stability
criteria
14. Turbulence
14.1 Overview
14.2 The Transition to Turbulence
Flow past a Cylinder
14.3 Semi-Quantitative Analysis of Turbulence: weak turbulence; turbulent diffusivity;
relationship to vorticity; Kolmogorov spectrum
14.4 Turbulent Boundary Layers: profile of a turbulent boundary layer; instability of
a laminar boundary layer; the flight of a ball
14.5 The Route to Turbulence
Onset of Chaos: Couette flow; Feigenbaum sequence
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15. Waves
15.1 Overview
15.2 Gravity Waves on Surface of a Fluid:
capillary waves; Helioseismology
deep water waves; shallow water waves;
15.3 Nonlinear Shallow Water Waves and Solitons: Korteweg-deVries equation; phys-
ical effects in the kdV equation; single solitoh solutions; two solitoh solution;
solitons in contemporary physics
15.4 Rotating Fluids: equations of fluid dynamics in a rotating reference frame;
geostrophic flows; Taylor-Proudman theorem; Ekman pumping; Rossby waves
15.5 Sound Waves; sound generation
16. Supersonic Flow
16.1 Overview
16.2 Equations of Compressible Flow
16.3 Stationary, Irrotational Flow: quasi-one-dimensional flow; setting up a stationary
transonic flow; rocket engines
16.4 One Dimensional, Time-Dependent Flow: Riemann invariants; shock tube
16.5 Shock Fronts: shock jump conditions in a perfect gas; Mach cone
16.6 Similarity Solutions
Sedov-Taylor Blast Wave: atomic bomb; supernovae
17. Convection
17.1 Overview
17.2 Heat Conduction
17.3 Boussinesq Approximation
17.4 Rayleigh-Bernard Convection
17.5 Convection in Stars
17.6 Double Diffusion
Salt Fingers
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18. Magnetohydrodynamics
18.1 Overview
18.2 Basic Equations of MHD: induction equation; dynamics; boundary conditions;
magnetic field and vorticity
18.3 Magnetostatic Equilibria: controlled thermonuclear fusion;
tokamak
Z pinch;
theta pinch;
18.4 Hydromagnetic Flows: electromagnetic brake; MHD power generator; flow meter;
electromagnetic pump; Hartmann flow
18.5 Stability of Hydromagnetic Equilibria:
ergy principle
linear perturbation
theory; Z pinch; en-
18.6 Dynamos and Magnetic Field Line Reconnection: Cowling's theorem; kinematic
dynamos; magnetic reconnection
18.7 Magnetosonic Waves and the Scattering of Cosmic Rays
V. PLASMA PHYSICS
19. The Particle Kinetics of Plasmas
19.1 Overview
19.2 Examples of Plasmas and their Density-Temperature Regimes: ionization bound-
ary; degeneracy boundary; relativistic boundary; pair production boundary; ex-
amples of natural and man-made plasmas
19.3 Collective Effects in Plasmas: Debye shielding; collective behavior; plasma oscil-
lations and plasma frequency
19.4 Coulomb Collisions: collision frequency; Coulomb logarithm; thermal equilibra-
tion times
19.5 Transport Coefficients: anomalous resistivity and anomalous equilibration
19.6 Magnetic field: Cyclotron frequency and Larmor radius;
approximation; conductivity tensor
validity of the fluid
19.7 Adiabatic invariants: homogeneous, time-independent magnetic field; homo-
geneous time-independent electric and magnetic fields; inhomogeneous time-
independent magnetic field; a slowly time-varying magnetic field
x
20. Waves in Cold Plasmas: Two-Fluid Formalism
20.1 Overview
20.2 Dielectric Tensor, Wave Equation, and General Dispersion Relation
20.3 Wave Modes in an Unmagnetized Plasma: two-fluid formalism
20.4 Wave Modes in a Cold, Magnetized Plasma:
relation
dielectric tensor and dispersion
20.5 Propagation of Radio Waves in the Ionosphere
20.6 C, MA Diagram for Wave Modes in (',old, Magnetized Plasma
20.7 Two-Stream Instability
21. Kinetic Theory of Warm Plasmas
21.1 Overview
21.2 Basic Concepts of Kinetic Theory and its Relationship to Two-Fluid Theory:
distribution function and vlasov equation; relation to two-fluid theory; Jeans'
theorem
21.3 Electrostatic Waves in an Unmagnetized Plasma and Landau Damping; formal
dispersion relation; two-stream instability; the Landau contour; dispersion re-
lation for weakly damped or growing waves; Langmuir waves and their Landau
damping; ion acoustic waves and conditions for their Landau damping to be weak
21.4 Stability of Electromagnetic Waves in an Unmagnetized Plasma: stability; parti-
cle trapping
21.5 N-Particle Distribution Function
22. Nonlinear Dynamics of Plasmas
22.1 Overview
22.2
Quasi-Linear Theory in Classical Language: classical derivation of the theory;
summary of the theory; conservation laws; generalization to three dimensions
22.3 Quasilinear Theory in Quantum Mechanical Language: fundamental equations
and their interpretation; relationship between classical and quantum formula-
tions; inhomogeneous plasmas; generalization to other processes
22.4 Quasilinear Evolution of Unstable Distribution Function:
instability of streaming cosmic rays
The Bump in Tail:
22.5 Parametric Instabilities
22.6 Solitons and Collisionless Shock Waves
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VI.
GENERAL RELATIVITY
23. From Special to General Relativity
23.1 Overview
23.2 Special Relativity Once Again: geometric, frame-independent formulation; iner-
tial frames and components of vectors and tensors; physical laws; light speed, the
interval, and spacetime diagrams
23.3 Differential Geometry in General Bases and in C, urved Manifolds: nonorthonor-
real bases; vectors as differential operators; tangent space; commutators; differ-
entiation of vectors and tensors; connection coefficients; integration
23.4 Stress-Energy Tensor Revisited
23.5 Proper Reference Frame of an Accelerated Observer
24. Fundamental Concepts of General Relativity
24.1 Overview
24.2 Local Lorentz Frames, the Principle of Relativity, and Einstein's Equivalence
Principle
24.3 The Spacetime Metric, and Gravity as a Curvature of Spacetime
24.4 Free-fall Motion and Geodesics of Spacetime
24.5 Relative Acceleration, Tidal Gravity, and Spacetime Curvature: Newtonian de-
scription of tidal gravity; relativistic description of tidal gravity; comparison of
descriptions
24.6 Properties of the Riemann curvature tensor
24.7 Curvature Coupling Delicacies in the Equivalence Principle,
gravitational Laws of Physics in Curved Spacetime
and some Non-
24.8 The Einstein Field Equation
24.9 Weak Gravitational Fields: Newtonian limit of general relativity; linearized the-
ory; gravitational field outside a stationary, linearized source
25. Relativistic Stars and Black Holes
25.1 Overview
25.2 Schwarzschild's Spacetime Geometry
25.3 Static Stars: Birkhoff's theorem; stellar interior; local energy and momentum
conservation; Einstein field equations; stellar models and their properties
xii
25.4 Gravitational Implosion of a Star to Form a Black Hole
25.5 Spinning Black Holes: The Kerr Spacetime: motivation conservation laws for
mass, momentum, and angular momentum; the Kerr metric; dragging of inertial
flames; light-cone structure and the horizon; evolution of black holes- rotational
energy and its extraction
25.6 The Many-Fingered Nature of Time
26. Gravitational Waves and Experimental Tests of General Relativity
26.1 Overview
26.2 Experimental Tests of General Relativity: equivalence principle, gravitational
redshift, and global positioning system; perihelion advance of Mercury; gravita-
tional deflection of light, Fermat's principle and gravitational lenses; Shapiro time
delay; frame dragging and Gravity Probe B; binary pulsar
26.3 Gravitational Waves and their Propagation: the gravitational wave equation; the
waves' two polarizaitons, + and x; gravitons and their spin; energy and momen-
tum in gravitational waves; wave propagation in a source's local asymptotic rest
frame; wave propagation via geometric optics; metric perturbation and TT gauge
26.4 The Generation of Gravitational Waves: multipole-moment expansion; quadru-
pole moment formalism; gravitational waves from a binary star system; detection
of gravitational waves
26.5 The Detection of Gravitational Waves: [not yet written]
26.6 Sources of Gravitational Waves: [not yet written]
27. Cosmology
27.1 Overview
27.2 Homogeneity and Isotropy of the Universe
Robertson-Walker Line Element
27.3 The Stress-energy Tensor and the Einstein Field Equation
27.4 Evolution of the Universe: constituents of the universe cold matter, radiation,
and exotic matter; the vacuum stress-energy tensor; evolution of the densities;
evolution in time and redshift; physical processes in the expanding universe
27.5 Observational C, osmology: parameters characterizing the universe; local Lorentz
frame of homogenous observers near Earth; Hubble expansion rate; big-bang nu-
cleosynthesis; density of cold dark matter; radiation temperature and density;
anisotropy of the CBR: measurements of the Doppler peaks; age of the universe
constraint on the exotic matter; magnitude-redshift relation for type Ia super-
novae confirmation that the universe is decelerating
27.6 The Big-Bang Singularity, Quantum Gravity and the Intial Conditions of the
Universe
xiii
27.7 Inflationary Cosmology
