# Electrodynamics on spacetime – A summer school not only for phyics students

This summer school is a continuation of the summer schools in 2015 and 2017, but it can be enjoyed as a standalone experience as well. The topic for this year is the theory of electromagnetism using the framework of spacetime models. The prevalent feature of this framework is that it allows for a treatment that is manifestly independent of reference frames. Mathematical precision is paramount in this summer school. The language of instruction is Hungarian.

## Topics

**I. Mathematical tools**Borel sets, measures, integral theorems, submanifolds of affine spaces and their Lebesgue measures. Distributions: basics, differentiation, convolution, Poincaré's lemma, multiplication, depolarization, distributions connected to submanifolds of spacetime, fundamental solutions for the Poisson equation and the d'Alembert equation.**II. Electrostatics**Electric quantities: charge distribution, dipole distribution, electric field. Electrostatic Maxwell equations: differential and integral form. Coulomb potential and Coulomb field of a charge density and of a dipole density Symmetry properties. Special examples. Boundary conditions. Force lines, equipotential sets. Conductors in an electric field: charge separation, insulators in an electric field, polarization. The difference between D and ϵE. Force and energy densities. Direct current.**III. Magnetostatics**Magnetic quantities: moment distribution, magnetic field. Magnetostatic Maxwell equations: differential and integral form. Biot–Savart potential and Biot–Savart field of a current distribution and of a moment distribution. Symmetry properties. Special examples. Boundary conditions. Magnetizable bodies in a magnetic field, magnetizing. The difference between H and 1/μ B. Force and energy densities.**IV. Electromagnetic processes**Charge-current density, dipole moment density, electromagnetic field. Maxwell's equations. Point charge: retarded proper time, Liénard–Wiechert potential and Liénard–Wiechert field of a point charge and a point diple moment. Electromagnetic radiation, plane waves. Energy-impulse relations in the electromagnetic field. Radiative backreaction of a point charge, the Lorentz–Dirac equality. Interactions? Electromagnetic field in a medium, dissipation.

The participants will get a printout of the script used in the summer school (in Hungarian).

## Organizational details

**When:**7th July to 13th July 2019 (Sunday to Saturday)**Where:**Somogysimonyi, Hungary**How to get there:**take a public bus (Volán busz) to Zalakomár. The organizers will take care of the transfer from there.**Lecturers:**Tamás Matolcsi; Tamás Fülöp, András László, Áron Szabó, Péter Ván**Program:**two lectures in the morning, two lecture in the afternoon, exercises in the evening; excursion, elective mornig sport**How much:**25,000 HUF until 31 May, afterwards 30,000 HUF. Please transfer the fee to ETTE (Egyesület a Tudomány és Technológia Egységéért), IBAN HU75 11600006-00000000-19801517, BIC/SWIFT: GIBAHUHBXXX. Please write your name in the remark field.- Full PENSION: accommodation for 6 nights, meals (6 days, twice cold, once warm), program and background material (print and pdf).

**Webpage:** http://indico.kfki.hu/e/elektrodinamika2019

**Organizers:** MTA Wigner Research Centre, ETTE

### Responsible organisations

MTA WIGNER Research Centre for Physics, Society for the Unity of Science and Technology.