Winter-Semester 2021/22

Foundations and Applications of Special Relativity

Lectures (weekly, start Thursday 14.10.2021)

Thursdays 08:15 - 09:45, Building 3701 (ITP), Room 268 (großer Seminarraum)
Fridays 08:15 - 11:45, Building 3701 (ITP), Room 268 (großer Seminarraum)
An interactive site map for all lecture- and seminar-rooms can be found here.  

Exercises (weekly, start Wednesday 20.10.2019)

Wednesdays 16:15 - 17:45, Building 3701 (ITP), Room 269 (kleiner Seminarraum)
In the weekly extercise classes we will present and discuss the solutions of the problems on the sheet that was distributed here on the week before. Students are expected to present their solutions upon request or register for their presentation.  


The Lecture is structured into (4+2) hours weekly, meaning that there are 2 lectures of 90 minutes each on Thursdays and Fridays and, in addition, an exercise class of 90 minutes on Wednesdays.

Certificates of study and examination (Studien- und Prüfungsleistung); module assignments; ECTS points

An ungraded certificate of study (Studenleistung) will be given to participating students depending on their performance in the problem-solving classes. This includes a complete and correct presentation of at least one problem. In addition, a graded certificate of examination (PrÃŒfungsleistung) will be given after an individual oral examination of about 40 minutes. This lecture can exclusively account for either the BSc-module "moderne Aspekte der Physik" (1601) or for the MSc-module "Ausgewählte Themen moderner Physik" (1621). The number of ECTS points for this lecture is 8 (one for each weekly hour -- 45 minutes -- of lectures and two for exercises.

Contents and prerequisites

Special Relativity (SR) underlies all modern theories of fundamental interactions in which gravity can be neglected. In particular, it undelies the standard model of elementary particle physics and is responsible for, e.g., the classification of elementary particles in terms of "mass" and "spin". It is also directly responsible for other fundamental results, like the theorems on the correleation between spin and statistics and that on CPT-invariance. But despite its fundamental inmportance, SR is usually not considered worthy its own lecture course, despite the fact that, on a closer look, it is highly non-trivial, both conceptually and mathematically. In this lecture we will start from scratch and explain where SR came from and what its implications are. To this end, we will discuss the structure of space and time, or space-time, in pre-SR physics, explain the changes implied by SR together with the the crucial experiments enforcing this change, and then turn to the new physics implied by SR. This is a rather long but fascinating story, containing many twists and turns that are almost never mentioned depsite of their essential physical relevance. Necessary pre-requisites are a basic knowledge in Newtonian Mechnics and Electrodynamics, as well as no fear of contact aganist some abstact mathematical concepts that will be of immense help to us in fixing and structuring our physical ideas. More precisely, we will need notions like sets, groups, group actions, vector spaces, dual vector spaces, tensor products between vector spaces, representations of groups, affine spaces, and various algebraic and geometric strctures on such objects. In parts, we will also need some differential geometry. A list of tentative topics is give below. It will be completed as we will go along.


  1. Dynamical principles of Newtonian mechanics. The law of inertia and the affine structure of space-time.
  2. Groups and maps between them, group actions on sets, linear representations of groups.
  3. Affine spaces and their structure-preserving maps (automorphisms).
  4. The Galilei group, its structure, and its geometric underpinning.
  5. The principle of relativity in Newtoinian mechanics.
  6. The principle of relativity in Electrodynamics.
  7. Electrodynmics of moving bodies: From Hertz to Einstein.
  8. Crucial experiments and the question of whether there is an "aether".
  9. Einstein's 1905 solution.
  10. The Lorentz- and Poincaré groups.
  11. Lorentz-contraction and time-dilation demystified.
  12. The Poincaré group and its geometric underpinning: Mikowski space.
  13. Decomposition of Lorentz transformations: "velocity addition" and "Thomas precession".
  14. A group-theoretic comparison between the Galilei and the Poincaré group.
  15. Adapting mechanics to SR.
  16. Electrodynamics and SR


This lecture I will proceed by following my own script which can be downloaded here. The script is divided in two parts. The first part is essentially finished and is meant to provide the background of what is actually meant to be the core of this lecture, which is the more technical 2nd part. That second part is in the process of writing and will almost continuosuly be expanded as we go along. How much time we will spend on Part I (the background) depends on the experience in class.

Textbooks and other texts

Here are some suggestions for further reding:

  • Roman Sexl und Helmuth Urbantke: Relativity, Groups, Particles. Special Relativity and Relativistic Symmetry in Field and Particle Physics. Springer Verlag, Wien (2001): lookup here. A classic text that stresses the applications of SR to particle physics. It provides much information on group- and representation-theoretic aspects and is full of interesting remarks and details worth considering.
  • Brian C. Hall: Lie Groups, Lie Algebras, and Representations. Springer Verlag, New York (2003).
  • Norbert Dragon: Geometrie der Relativitätstheorie. Lookup here.
  • Domenico Giulini: Algebraic and geometric structures of Special Relativity. Download here.


  • Albert Einstein: Zur Elektrodynamik bewegter Körper (engl. Electrodynamics of moving bodies), Annalen der Physik, Vol. 17 (1905). Download german original german original and english translation.


Prof. Dr. Domenico Giulini