THEORETICAL PHYSICS

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.

Textbooks:

• A. Messiah: Mèchanique quantique, Dunod, Paris, 1969.
• N. N. Bogoliubov and D. V. Shirkov: Quantum Fields, London, 1983.
• S. Weinberg: The Quantum Theory of Fields, Cambridge University Press, New York, 1995.
• Lecture notes (in Italian).