OVERVIEW

Theoretical physics provides the tools for understanding modern theories of fundamental interactions.

AIMS AND CONTENT

LEARNING OUTCOMES

Provide the student with the basics of relativistic electrodynamics and familiarize him with mechanics the quantum systems of many bodies treated in the second quantization.

AIMS AND LEARNING OUTCOMES

To provide the student with the methods to understand (1) the formulation of mechanics based on the principle of minimum action and the relationship between symmetries and laws of consecration; (2) the general theory of the scalar, vectorial and spinorial fields in Minkowski space-time; (3) the covariant formulation of classical electrodynamics; (4) the quantum theories of many-body systems and the second quantization method; (5) the basic principles of quantum electrodynamics with applications to quantum optics; (6) relativistic wave equations with particular reference to the Dirac equation. The expected learning outcomes relate to the student's ability to perform calculations and solve (quantitatively) problems on the 6 points indicated above.

PREREQUISITES

Non-relativistic quantum mechanics and mathematical methods of basic physics.

TEACHING METHODS

Traditional

SYLLABUS/CONTENT

Role of action in classical mechanics
 Lagrange function and Euler-Lagrange equations
 Hamilton function and canonical equations
 Continuous systems and local fields
 Hamilton's action principle for particles and local fields
 
 Symmetries
 Rotations and tensors
 Rotations and spinors
 Continuous symmetries and Noether theorem for particle systems
 Continuous symmetries and Noether theorem for local fields
 Gauge invariance
 Aharonov-Bohm effect
 
Relativistic invariance
Inertial systems, Newton's first law and Lorentz transformations
Lorentz transformations and tensors
Lorentz transformations and spinors
Correspondence between Lorentz and  transformations SL(2, C)
Spinor as a 4-vector light type
Spatial inversion and chirality

Relativistic fields
Differential and integral operations on tensor fields
Scalar field
Maxwell field
Weyl and Dirac fields
 
Classic linear systems
Analysis in normal ways of the scalar field
Analysis in normal ways of the Maxwell field
Spectral distribution of radiation in a cavity
 
Quantum linear systems
The quantum harmonic oscillator
Weyl operator
Coherent states
Linear response, Kubo formula and interaction representation
 
Quantum Klein-Gordon field
The real scalar field
A quantum analogue of the normal rope mode
Commutations relations and Feynman propagator
  
Maxwell quantum field
The electromagnetic field as a quantum system
Casimir effect
Rudiments of quantum optics
Stimulated emission
Spontaneous emission
Photon detectors
Correlation and interference functions
  
  
General formalism of second quantization
Second quantization of the Schrödinger field
Operators in second quantization
Dynamics of bosons and fermions
Quasi-particles and holes for a system of fermions
Interaction between fermions mediated by bosons
Second quantization of the Dirac field

RECOMMENDED READING/BIBLIOGRAPHY

Landau - Lifsits  Fisica Teorica 2 - Field Theory

Landau - Lifsits  Fisica Teorica 4 -  Relativistic Quantum Theory

Ballentine - Quantum Mechanics  

TEACHERS AND EXAM BOARD

Exam Board

PIERANTONIO ZANGHI' (President)

NICOLA MAGGIORE

NICODEMO MAGNOLI

LESSONS

LESSONS START

From 25 September 2017

Class schedule

THEORETICAL PHYSICS

EXAMS

EXAM DESCRIPTION

Written test; possible oral exam.

ASSESSMENT METHODS

The aim of the course is to provide students with the ability to perform calculations and solve (quantitatively) problems. For this reason, the fundamental component of the exam is written, in which the student is asked to demonstrate his ability to calculate and explicitly solve problems. After many years of teaching, it is my belief that the oral examination may constitute only a small correction to the judgment that comes from the writing. It must be emphasized that it is not at all obvious that this correction must be in a positive sense. For this reason, the student can request to have the written grade confirmed as final grade.

Exam schedule