CODE 114704 2024/2025 6 cfu anno 1 FISICA 9012 (LM-17) - GENOVA 6 cfu anno 3 FISICA 8758 (L-30) - GENOVA FIS/02 Italian GENOVA 1° Semester

## OVERVIEW

Classical Electrodynamics has credit value 6 and it is taught in the first semester of the third year of the Laurea. Its main goal is to develop the covariant formalism for electrodynamics and to illustrate some of its physical applications, with particular emphasis on radiation phenomena.

Lectures are taught in italian. Learning material is available on AulaWeb.

## AIMS AND CONTENT

### LEARNING OUTCOMES

The teaching aims to introduce the covariant formalism for electrodynamics and develop its main physical applications, with special emphasis on purely relativistic phenomena, such as radiation. After introducing the functional method for a generic relativistic field theory, the general solution of Maxwell's equations, electromagnetic fields generated by a moving charge, emitted radiation, development in multipoles, spectral analysis of radiation, and the effects of radiation on the motion of emitting particles will be studied.

### AIMS AND LEARNING OUTCOMES

Electromagnetic laws are left invariant by the Lorentz transformations of Special Relativity. The teaching unit will introduce the covariant formalism which makes this invariant manifest. The same formalism also simplifies the solution of several physical problems, and in particular of those that follow directly from the relativistic nature of the theory, like radiation. Some of the main phenomenological consequences of electrodynamics (Larmor's law, Thomson scattering, synchrotron and Cerenkov radiation, radiation reaction) will be illustrated, alongside with the conceptual and methodological tools needed to study general relativistic field theories (lagrangian formalism, Noether's theorem, Cauchy problem, Green's function method).

The students will develop the skills needed to apply the covariant formalism to the study of electromagnetic phenomena and will acquire the conceptual basis of radiation and its main physical consequences.

### PREREQUISITES

Classical Electromagnetism and basic Special Relativity.

### TEACHING METHODS

Traditional: chalk and blackboard. Home assignments will be handed out weekly and their solution will be verified during the final oral exam.

### SYLLABUS/CONTENT

• A short review of Special Relativity: Poincarè transformations and their infinitesimal form, tensor calculus, elements of relativistic dynamics.
• Maxwell's equation and Lorentz force in covariant form; the electromagnetic tensor, the vector potential and Bianchi identities.
• The Lagrangian formalism and the variational method for relativistic field theories. The action of electrodynamics.
• Conservation laws, Noether's theorem, the canonical and the symmetric energy-momentum tensor.
• The Cauchy problem for Maxwell's equations and the degrees of freedom of the electromagnetic field. Electromagnetic waves.
• Green's functions and the field generated by a charge in arbitrary motion (Lienard-Wiechert potentials).
• Radiation: general results and multipole expansion. Dipole approximation and Larmor's formula. Electric quadrupole and magnetic dipole.
• Thomson scattering.
• Radiation reaction and the Lorentz-Dirac equation.
• A brief introdution to magnetic monopoles.

• K. Lechner, Elettrodinamica Classica, Springer
• L. Landau, E. Lifsists, Fisica Teorica 2. Teoria dei Campi, Editori Riuniti

## LESSONS

### LESSONS START

Check the calendar at

https://corsi.unige.it/corsi/9012/studenti-orario

### Class schedule

The timetable for this course is available here: Portale EasyAcademy

## EXAMS

### EXAM DESCRIPTION

Oral exam. During the exam the student will also be asked to discuss the solution of one of the home assignments.

### ASSESSMENT METHODS

A list of problems will be handed out weekly. To verify that students are able to apply the techniques of the covariant formalism to problem solving, students will be asked to present the solution of one of the home assignments during the oral exam. The exam also aims at assessing the knowledge and comprehension of the results derived in class.

### FURTHER INFORMATION

Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Sergio Di Domizio (sergio.didomizio@unige.it), the Department’s disability liaison.