### THEORETICAL PHYSICS

**1st module**

**(one semester, about 33 hours)**

**Prof. Marco Toller**

**A.A. 1998/99**

- Recall of relativistic mechanics and electromagnetism.
- Problems with the Klein-Gordon equation for the wave function.
- The Dirac equation minimally coupled with the electromagnetic field.
- Its non-relativistic limit; spin and magnetic moment; the relativistic hydrogen atom.
- Many particle systems; Fock spaces and free fields: commutation relations.
- Application to non relativistic systems; one and two-particle operators; cluster expansion.
- Equilibrium states at non-vanishing temperature and density.
- Quantum relativistic free scalar field; vacuum fluctuations; local
commutativity; spin and statistics; antiparticles.
- Conservation laws and local currents.
- Interaction picture; scattering operator; perturbative series and time ordering; Feynman graphs.
- 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).