Trinity College Dublin

Classical Fields and Electrodynamics

• Classical Lagrangian for a discrete system, Lagrangian density for a field
• Hamilton's variational principle, Lorentz invariance, time & space reversal
• Covariant field theory, tensors, scalar fields and the four-vector potential
• The Lorentz force, charged particle interaction, antisymmetric field tensor
• Lagrangian density for a free vector field; Maxwell equations for E and B
• Gauge invariance, the Lorenz gauge, charge conservation, four-currents
• Canonical stress tensor; conserved, traceless & symmetric stress tensor
• Particle and field energy-momentum & angular momentum conservation

• Solving Maxwell's equations; Green functions for Laplacian, d'Alembertian
• Liénard-Wiechert potential; velocity, acceleration fields for moving charge
• Radiation theory; velocity and acceleration fields in terms of E & B and π
• Non-relativistic Larmor formulæ and relativistic Liénard radiation formula
• Linear & circular accelerated motion; radiation in constant magnetic field
• Angular distribution of relativistic radiation; electric & magnetic elements
• Introduction to radiation damping; decay of the radius for a circular orbit
• Envoi: quantum electrodynamics and chromodynamics; electroweak field

Recommended material

1. Classical Electrodynamics, J. David Jackson, John Wiley (3rd edition) 1998
2. Classical Theory of Fields, E. M. Lifshitz and L. D. Landau, Pergamon, 1962
3. Classical Field Theory, Francis E. Low, John Wiley (1st edition) 1997
4. Introduction to Electrodynamics, David J. Griffiths, Prentice-Hall, 1999
5. Web Physics 120, 121, 124: www.slac.stanford.edu/~mpeskin/#courses/

CFT pdf files

•     Course description
•     Solution to exercise 2
•     Tutorial exercise 3 for revision
•     Solution to ex. 3 and a bound on the photon mass
•     Conversion of units and the EM spectrum
•     Music of the spheres

This Web page  http://www.maths.tcd.ie/~nhb/432.php