MA3431 : Classical Field Theory

  1. Electrostatics; Green's Theorem; Solution by Green functions.

  2. Spherically symmetric problems; Multipole expansion; Magnetostatics.

  3. Maxwell equations; Gauge invariance; Transformation properties.

  4. Lorentz invariance; Poincaré Lie algebra; Scalar, vector and tensor representations.

  5. Hamilton's variational principle, Lagrangian for relativistic particle.

  6. The Lorentz force, charged particle interaction, antisymmetric field tensor.

  7. Covariant field theory, tensors, scalar fields and the four-vector potential.

  8. Lagrangian density for a free vector field; Symmetry properties.

  9. Canonical stress tensor; conserved, traceless & symmetric stress tensor.

  10. Particle and field energy-momentum & angular momentum conservation.

Course Overview

Course Details

Instructor: Tristan McLoughlin


  1. Tuesday 12:00-12:50 & 14:00-14:50 (Synge Theatre)

  2. Wednesday 14:00-14:50 (SNIAM)

Office hours/Tutorials: TBA or upon appointment (contact by email beforehand)


  1. 1.Classical Electrodynamics, J. David Jackson, John Wiley (3rd edition) 1998.

  2. 2.Classical Theory of Fields, L. D. Landau & E. M. Lifshitz, Heinemann, 1972.


  1. Homework counts for 15% of final grade. Each set is handed out on Wednesday and due the following Wednesday at the beginning of class. Collaboration is allowed however each student should hand in their own version of the solutions.

  2. Final exam counts for the remaining 85%.

Image from Nasa