THEORICAL PHYSICS (f)

1^o Modulo

Luciano Vanzo

Scope of the course:

Covered arguments :

1. Many-particle systems and quantum field theory: symmetry properties under particles exchange; bosons and fermions; Fock space; creation and annihilation operators; canonical commutation relations; one and two-particles operators; non relativistic systems; quantized fields as operator-valued distributions; connected expectation values; generating functionals; property of the vacuum in non relativistic field theory.
2. Equilibrium states with non zero temperature and density; grand-canonical ensemble; fields expectation values; the infinite volume limit; applications to ideal quantum gases; Bose-Einstein condensation; spontaneous symmetry breaking.
3. Relativistic wave equations: the Klein-Gordon equation and its difficulties; the Dirac equation; relativistic invariance of Dirac equation; negative energy states and hole theory; minimal coupling to electromagnetic field; non relativistic limit; spin and magnetic moment of the electron; spectrum of the hydrogen atom; fine structure.
4. Relativistic free quantum fields; spinless relativistic particles; the quantum scalar field; vacuum fluctuations; local commutativity and commutation relations; vacuum expectation values and normal products; spin-statistics connection and anti-particles; spinning relativistic particles; the quantum spinor field; local commutativity and anti-commutation relations; spin statistics connection; vector particles.
5. Introduction to perturbative methods; interaction representation; perturbative expansion of the scattering operator and time-ordered products; perturbative expansion of Green functions; effect of interactions on the vacuum and the infinite volume limit.

Bibliography:

• A. Messiah: Mèchanique quantique, Dunod, Paris, 1969.
• N. N. Bogoliubov and D. V. Shirkov: Quantum Fields, Benjamin/Cummings, London, 1983.
• S. Weinberg: The Quantum Theory of Fields, Vol.1 Cambridge University Press, New York, 1995.

Examination:

Links: