OVERVIEW

This course is the natural continuation of the course "Quantum Physics". The applications of interest of ordinaruy quantum mechanics require familiarity with specific techniques for the study of systems with many degrees of freedom. The main purpose of this course is poroviding the student with the basic ideas of these techniques and illustrating the relevant applications, both in a many-body, non relativistic context and in the context of the relativistic extension of quantum physics.

AIMS AND CONTENT

LEARNING OUTCOMES

Providing the student with basis concepts in relativistic electrodynamics, and with quantum mechanics of many-body systems in the context of second quantization.

AIMS AND LEARNING OUTCOMES

The student will extend and upgrade his/her knowledge in quantum mechanics

The second quantization formalism will be illustrated in details and applied to relevant physical situations, both in non-relativistic and relativistic cases.

The quantization of electromagnetic fields and the relativistic description of quantum mechanics in simple cases will also be discussed.

PREREQUISITES

Classical physics

Non-relativistic quantum mechanics

Special theory of relativity

TEACHING METHODS

Traditional lectures at the blackboard; six hours per week.

SYLLABUS/CONTENT

1. Second quantization

- Identical particles
- Second quantization of a system of identical bosons
- Second quantization of a ststem of identical  fermions
- Perturbation theory in the second quantization formalism.

2. Phonons

- One dimensional coupled oscillators; normal modes

- Quantization.

3. The electromagnetic field

- The classical electromagnetic field; normal modes
- Quantization of the electromagnetic field

- Coherent states
- Matter-radiation interaction
- Emission and absorption of radiation.

- Thompson Scattering.

4. Classical field theory

- Symmetries
- Noether theorem and conservation laws

5. Spin 0 and spin 1/2 quantum fields

- The real Klein-Gordon field
- The complex Klein-Gordon field. Particles and antiparticles.

- The Dirac field.

6. Quantum field interactions

- Yukawa interaction and electromagnetic interaction.
- Fermi's golden rule. LSZ reduction formlua. Interaction representation.

- Cross sections and decay rates.
 

RECOMMENDED READING/BIBLIOGRAPHY

Landau, Lifsitz 2 - Field theory

Landau, Lifsitz 3 - Quantum mechanics

Landau, Lifsitz 4 - Relativistic quantum theory

Gerry, Knight - Introductory Quantum Optics, Cambridge

Becchi, Ridolfi - An Introduction to relativistic processes and the standard model of electroweak interactions

Becchi - Appunti di fisica teorica

Maiani - Meccanica quantistica relativistica e introduzione alla teoria dei campi

TEACHERS AND EXAM BOARD

Exam Board

GIOVANNI RIDOLFI (President)

NICOLA MAGGIORE

NICODEMO MAGNOLI

SIMONE MARZANI

LESSONS

LESSONS START

September 24, 2018

Class schedule

THEORETICAL PHYSICS

EXAMS

EXAM DESCRIPTION

Written test + interview

ASSESSMENT METHODS

In the written test the student will be asked to solve two problems. The interview will last around 30 minutes.

Exam schedule