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PHYSICS 722, ADVANCED CLASSICAL THEORETICAL PHYSICS


TENTATIVE SYLLABUS, SPRING, 1999

The course is divided into three units with different themes and emphases:
 
Unit 1:  RELATIVITY AND PARTICLE ELECTRODYNAMICS
Unit 2:  RADIATIVE PROCESSES AND CLASSICAL FIELDS
Unit 3:  HAMILTONIAN MECHANICS, APPROXIMATIONS AND APPLICATIONS.

 

Albert Einstein
1905		 James Clerk Maxwell

UNIT 1: RELATIVITY AND PARTICLE ELECTRODYNAMICS

Week Lec. Date Subjects
1 1 Jan. 20  Jackson, Chaps. 11 and 12. Relativity: notation, matrix approach, properties of the transformation matrices, the Lorentz group SO(1,3).
2 22  Generators of infinitesimal transformations, algebraic properties, exponential representations of SO(1,3), rapidity and boosts, hyperbolic geometry.
2 3 Jan. 25  4 velocity, the energy-momentum 4-vector, relativistic kinematics, geometric interpretation, examples.
4 27  Wigner rotations and the Thomas precession. The covering group SL(2,C), 2 × 2 matrix representations.
Hw. 1 5 29  Maxwell's equations, the Lorentz force equation. Covariant and contravariant 4 vectors, the electromagnetic potential and current 4 vectors.
3 6 Feb. 1  The electromagnetic field tensor F, the dual field tensor *F, Maxwell's equations in covariant form.
7 3  Transformation properties of E and B, the field of a rapidly moving particle.
Hw. 2 8 5  Invariants of the fields. The electromagnetic energy-momentum tensor, conservation laws.
4 8 Feb. 8  Energy-momentum flow in the electromagnetic field; particles with spin, the Bargmann-Michel-Telegdi equation.
10 10  Particle motion in uniform E and B fields, use of invariants. Jackson, Chap. 13. Interactions of particles in matter, energy loss in ionizing collisions.
Hw. 3 11 12  Ionizing collisions, classical and quantum regimes, limits on the impact parameter, dE/dx for relativistic particles.
5 12 Feb. 15  Long distance effects in dielectrics; Fourier representations and frequency dependent fields, fields of a uniformly moving relativistic particle.
13 17  Frequency dependent expressions for the fields in terms of Bessel functions; energy flow and energy loss in a dielectric using the energy-momentum tensor; the density effect on dE/dx.
Hw. 4 14 19  Cherenkov radiation, transition radiation.
END OF UNIT 1
Amalie Emmy Noether

UNIT 2: RADIATIVE PROCESSES AND CLASSICAL FIELDS

Week Lec.   Date   Subjects
6 15 Feb. 22  Jackson, Chap 14. Green's functions, the Liénard-Weichert potentials, retarded fields, geometric interpretation.
16 24  HOUR EXAM IN CLASS ON THE MATERIAL IN UNIT 1, CHAPS. 11-13.6 IN JACKSON, PLUS LECTURE
17 26  The electromagnetic field tensor, near and far fields, radiation by accelerated particles, the radiative stress tensor, energy and momentum flow.
7 18 March 1  The Larmor power scalar, power radiated and observed, angular distribution of radiation, examples.
19 3  Examples, scattering of radiation, Thomson scattering.
Hw. 5 20 5  Fourier description of radiation fields, angular and frequency distributions of radiation, approximations.
SPRING RECESS, MARCH 6-14
8 21  March 15  Synchrotron radiation, particles in magnetic fields.
22 17  Jackson, Chap. 15. Bremsstrahlung, particles subject to sudden accelerations, examples.
Hw. 6 23 19  Radiation for small accelerations, equivalent photon approximation, applications.
9 24 March 22  Bremsstrahlung, synchrotron radiation in the equivalent photon picture, Thomson scattering of equivalent photons.
25 24  Goldstein, Chaps. 12, 13: classical fields, Hamilton's principle, the Euler-Lagrange equations and boundary conditions for fields.
Hw. 7 26 26  Examples of classical fields: the string, membrane, elastic solids, gases.
10 27 March 29  Higher order Lagrangians, beams and plates, water waves.
28 31  Functional derivatives, Hamilton's equations for fields, Poisson brackets.
Hw. 8 29 April 2  Noether's theorem, symmetries and constants of the motion.
11 30 April 5  Examples, generators of symmetries, symmetry algebras, integrable systems.
31 7  Relativistic fields, the stress tensor; gauge transformations in electrodynamics.
END OF UNIT 2

     
William Rowan Hamilton Henri Poincaré
1880

UNIT 3: HAMILTONIAN MECHANICS, APPROXIMATIONS AND APPLICATIONS

Week Lec.   Date   Subjects
Hw. 9 32 April 9  Hamiltonian mechanics, the symplectic structure of mechanics, canonical transformations.
12 33 12  Qualitative description of motion, phase space, exponential maps; Lagrange brackets.
34 14  The Cartan and Poincaré invariants, Liouville's theorem, Poincaré recurrences.
35 16  HOUR EXAM IN CLASS ON THE MATERIAL IN UNIT 2, CHAPS. 14-15 IN JACKSON AND CHAPS. 12-13 IN GOLDSTEIN, PLUS LECTURE
13 36 April 19  Goldstein, Chap. 10: Transformation to constant coordinates, generating functions, Hamilton-Jacobi theory, separation of variables, examples.
37 21  Action and angle variables, oscillator, separable systems, multiply periodic systems, invariant tori.
Hw. 10 23  Goldstein, Chap. 11: Fourier series, canonical perturbation theory.
14 38 April 26  Examples; secular perturbations.
39 28  Adiabatic invariants, examples and applications.
Hw.11 40 30  Stability of motion, Lyapunov exponents; parametric resonance.
15 41 May 3  Periodic potentials, mappings at a period, qualitative analysis of motion.
Hw. 12 42 5  Accelerators; the rings of Saturn.
END OF UNIT 3
Final May 14  FINAL EXAM MONDAY, MAY 10, 12:25 pm, EMPHASIS ON UNIT 3, GOLDSTEIN CHAPS. 10, 11 PLUS LECTURE

© Loyal Durand, 1998