## Summer Semester 2022

### Quantum Field Theory

This is the mandatory Quantum Field Theory course of the Master in Theoretical Physics at the University of Wrocław. It is tailored towards master and PhD students who are familiar with

- quantum mechanics
- electrodynamics
- special relativity
- quantum electrodynamics.

There are many good books on the subject, two of the classics are

- Peskin, Schroeder: An introduction to quantum field theory
- Weinberg: The Quantum Theory of Fields, Volume 1 & 2.

We will follow mostly the first one in the lectures and resort to Weinberg for details. There will be 2 hours of lectures and 2 hours of tutorials each week. For more information, please refer to the syllabus (in Polish) or contact me directly.

Additional material for the individual lectures, including the exercises which we discuss in the tutorials, is given below:

1

Reminder of spin 0 and 1/2 fields

2

Reminder of spin 1 fields, symmetries

3

Symmetries and groups

4

Dimensional analysis, regularisation (cutoff, dimensional, PV)

5

QED at one loop (self-energy, vacuum polarisation)

6

Renormalised perturbation theory of QED (1)

7

Renormalised perturbation theory of QED (2)

8

Superficial divergences and power counting, renormalisability ($\phi^4$, QED)

9

Renormalisation scale, $\beta$-function, RG flow

10

Path integral in QM, generating functional

11

Path integral for scalars, interactions, Feynman rules

12

Path integral for fermions

13

Path integral for spin-1 bosons, ghost fields

14

BRST symmetry, physical Hilbert space

15

Non-Abelian gauge theory, Feynman rules, QCD at one loop

### Lie Algebras and Groups

Lie algebras describe infinitesimal symmetries of physical systems. Therefore, together with their representation theory, they are extensively used in physics, most notably in quantum mechanics and particle physics. This course introduces semi-simple Lie algebras, their representation theory and the corresponding groups for physicists. As a major application, we discuss Grand Unified Theories (GUT). Moreover, we show how modern computer algebra tools like LieART can significantly help in all required computations throughout the course.

## Winter Semester 2013/2014

### String Theory I

This course introduces bosonic string theory in the elite master course "Theoretical and Mathematical Physics" at LMU Munich. This semester, it is taught by Dieter Lüst. In coordinating with Prof. Lüst, I prepare the excercises, grade them and discuss all solutions with the students in the tutorials. Below is a list of all exercises.

1

Light-cone coordinates and compact dimensions, exercise

2

Point particle action and reparameterization, exercise

3

The 2-sphere, exercise

4

Polyakov action and conformal transformations, exercise

5

Classical relativistic string, exercise

6

Virasoro algebra, exercise

7

Quantization of the relativistic string, exercise

8

Path integrals, ghosts and Grassmann numbers, exercise

9

Conformal field theory, exercise

10

Vertex operators and the complex plane, exercise

11

String compactification on the circle, exercise

12

String compactification on the torus, exercise

13

D-branes, exercise

## Summer Semester 2013

### Theoretical Mechanics

An introduction to classical mechanics for bachelor students at the LMU Munich, taught in German by Dieter Lüst. Due to a large number of participating students, there are multiple tutorials for this course, coordinated by James Gray. My responsiblity is to help James in preparing excercises and the exam in German and to give one of the tutorials. A list of all twelve excercises follows.

1

Vektoren und Kinematik, exercise

2

Die Newton’schen Axiome, exercise

3

Erhaltungsgrößen und die Newton’schen Axiome, exercise

4

Drehimpulserhaltung und Streuung, exercise

5

Flugbahn und Streuung, exercise

6

Orbits und der Runge-Lenz Vektor, exercise

7

Rotierende Koordinatensysteme, exercise

8

Starre Körper, exercise

9

Starre Körper und Lagrange-Gleichung erster Art, exercise

10

Lagrange-Formalismus, exercise

11

Lagrange-Formalismus II, exercise

12

Lagrange-Formalismus III, exercise