B2: Symmetry and Relativity

New material will appear here during the term. Older (and still very useful) material can be found on Prof Steane's page linked below.

The main change between the older and newer material is the order: fields and spinors have been moved into the middle, following Special Relativity, and before covariant electromagnetism. If there is time, there will be some further discussion of symmetry.

Lecture notes

Complete lecture notes (fixed typos, 1 Dec 2017)

Notes used/generated during the term (kept for reference):

  1. Outline, updated 27 Nov 2017
  2. Section 1, updated 25 Oct 2017
  3. Section 2, updated 25 Oct 2017
  4. Section 3, updated 25 Oct 2017 (Groups)
  5. Section 4, updated 2 Nov 2017 (Lorentz group)
  6. Section 5, updated 6 Nov 2017 (Poincare group and classical fields)
  7. Section 6, updated 6 Nov 2017 (Classical fields, EM)
  8. Section 7, updated 16 Nov 2017 (Radiation)
  9. Section 8, updated 21 Nov 2017 (Moving charges)
  10. Section 9, updated 23 Nov 2017 (Energy-momentum tensor)
  11. Section 10, updated 27 Nov 2017 (Noether's theorem)

Problem sets

Problem sets 1-4

Prof Steane's page also includes a list of relevant past exam questions, and two example spinor questions for exam revision.




Transformation properties of vectors in Newtonian and relativistic mechanics; 4-vectors; proper time; invariants. Doppler effect, aberration. Force and simple motion problems. Conservation of energy-momentum; collisions. Annihilation, decay and formation; centre of momentum frame. Compton scattering.

Transformation of electromagnetic fields; the fields of a uniformly moving charge. 4-gradient.The electromagnetic potential as a four-vector; gauge invariance, the use of retarded potentials to solve Maxwell's equations (derivation of functional forms of potentials not required).

Equations of particle motion from the Lagrangian; motion of a charged particle in an electromagnetic field.

Field of an accelerated charge; qualitative understanding of its derivation; radiated power, Larmor's formula. The half-wave electric dipole antenna.

3-d and 4-d tensors; polar and axial vectors; angular momentum; the Maxwell field tensor F(mu,nu) ; Lorentz transformation of tensors with application to E and B. Energy-momentum tensor of the electromagnetic field, applications with simple geometries (e.g. parallel-plate capacitor, long straight solenoid, plane wave).

2-spinors: rotation, Lorentz transformation and parity; classical Klein-Gordon equation [Non-examinable: Weyl equations; Dirac equation.]

J Tseng, 2 Dec 2017