1st module

(one semester, about 33 hours)

Prof. Marco Toller

A.A. 1998/99

  1. Recall of relativistic mechanics and electromagnetism.
  2. Problems with the Klein-Gordon equation for the wave function.
  3. The Dirac equation minimally coupled with the electromagnetic field.
  4. Its non-relativistic limit; spin and magnetic moment; the relativistic hydrogen atom.
  5. Many particle systems; Fock spaces and free fields: commutation relations.
  6. Application to non relativistic systems; one and two-particle operators; cluster expansion.
  7. Equilibrium states at non-vanishing temperature and density.
  8. Quantum relativistic free scalar field; vacuum fluctuations; local commutativity; spin and statistics; antiparticles.
  9. Conservation laws and local currents.
  10. Interaction picture; scattering operator; perturbative series and time ordering; Feynman graphs.
  11. The infinite volume limit and the Gell-Mann-Low formula for the relativistic Green functions.