Target skills and knowledge:
The course aims at introducing the techniques, based on the
non-relativistic quantum-field theory, which allow to determine
the statistical quantum-mechanical behavior of matter.
Examination methods:
Oral exam and home-work exercises.
Assessment criteria:
Basic theoretical knowledge and successful application of the formalism
to interesting physical systems.
Course unit contents:
Second-quantization formalism.
Single-particle and two-particle operators in second quantization.
Hamiltonian of Coulomb systems.
Two-point Green functions; expectation value of a single-particle
operator, ground-state energy, Lehmann representation.
Adiabatic theorem and perturbative evaluation of the ground state.
Wick's theorem and Feynman diagrams for fermionic systems at T=0.
Self-energy, polarization diagrams (effective interaction), Dyson's
equations.
Ground-state energy of the degenerate electron gas ("jellium" model)
in the ring approximation (RPA).
Linear-response theory; applications:
screening of the electric charge (Friedel oscillations),
plasma oscillations, electronic scattering cross section for the
inelastic electron scattering.
Interacting Bose systems at T=0.
Temperature Green's functions: Wick-Matsubara' theorem and
Feynman diagrams.
Textbooks (and optional supplementary readings)
A.L. Fetter, J.D. Walecka, Quantum theory of many-particle system.
New-York: MCGraw-Hill.
The course aims at introducing the techniques, based on the
non-relativistic quantum-field theory, which allow to determine
the statistical quantum-mechanical behavior of matter.
Examination methods:
Oral exam and home-work exercises.
Assessment criteria:
Basic theoretical knowledge and successful application of the formalism
to interesting physical systems.
Course unit contents:
Second-quantization formalism.
Single-particle and two-particle operators in second quantization.
Hamiltonian of Coulomb systems.
Two-point Green functions; expectation value of a single-particle
operator, ground-state energy, Lehmann representation.
Adiabatic theorem and perturbative evaluation of the ground state.
Wick's theorem and Feynman diagrams for fermionic systems at T=0.
Self-energy, polarization diagrams (effective interaction), Dyson's
equations.
Ground-state energy of the degenerate electron gas ("jellium" model)
in the ring approximation (RPA).
Linear-response theory; applications:
screening of the electric charge (Friedel oscillations),
plasma oscillations, electronic scattering cross section for the
inelastic electron scattering.
Interacting Bose systems at T=0.
Temperature Green's functions: Wick-Matsubara' theorem and
Feynman diagrams.
Textbooks (and optional supplementary readings)
A.L. Fetter, J.D. Walecka, Quantum theory of many-particle system.
New-York: MCGraw-Hill.