- Docente: Pier Luigi Silvestrelli

## Courses

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.

Category: A.A. 2019 - 2020 / Corsi di laurea magistrale / SC2382 - PHYSICS

- Docente: Pier Luigi Silvestrelli