Subatomic physics

Course goals

1. The student is able to work with covariant and contravariant vectors
2. The student is able to perform transformations between different inertial systems and to make calculations for decays and collisions between particles using relativistic mechanics
3. The student can calculate the equations of motion of both classical systems and relativistic fields equations. In addition the student can perform calculations on different types of relativistic fields.
4. The student can identify the building blocks of the Standard Model, the leptons, the quarks, the gauge bosons and their quantum numbers.
5. The student can distinguish the three different interactions of the Standard Model, the electromagnetic, the weak and the strong and their force carriers and is familiar with the conservation laws corresponding to the three interactions.
6. The student can use Fermi’s golden rule to perform calculations on scattering cross-sections and decay processes.
7. The student can compose and interpret Feynman diagrams for basic interactions between subatomic particles.
8. The student can explain the origin of the different terms in the QED and QCD Lagrangians and they can derive these terms using the correct gauge transformations.
9. The student can apply the Feynman rules for both QED and QCD to write down the matrix element of a basic process.
10. The student is able to make to make the connection between theory and experimental results.

Content

The lectures start with an introduction of the mathematical tools needed to study the underlying theory of particle physics. We will look at the Lagrangian formalism and at transformations between different inertial systems. We introduce the 4-vector notation and we will get a chance to make calculations for decays and collisions between particles using relativistic mechanics. After this we will make a side step to introduce the lagrangian formalism to find the equation of motion of a system. We will then study symmetries and conservation laws and we will familiarize ourselves with the building blocks of the Standard Model: the leptons, the quarks and the gauge bosons and their quantum numbers.
The second part of the lectures focuses on introducing the theoretical framework of the three pillars of the Standard Model: the electromagnetic, the weak and the strong interaction. We start with visualising different particle reactions with the help of Feynman diagrams. Then we dive deeper into the theoretical description of the three fundamental forces using relativistic field equations and gauge transformations. For each of the three forces, we make the connection between theory and the latest experimental results from state-of-the-art accelerators (e.g. the Large Hadron Collider at CERN).