# Bachelor thesis with Prof. Czakon in 2019

A model of multiple parton emissions

As is well known from electrodynamics, charged particles radiate electromagnetic waves if their trajectory is modified, as is the case in collisions. In particle physics, this radiation field must be described by multiple particle emissions. Such emissions are of great importance both in Quantum Electrodymics and in Quantum Chromodynamics. They are typically modelled with the help of a parton shower.

The purpose of this thesis is to develop a simplified parton shower program to simulate multiple particle emission and answer qualitative questions about the behaviour of cross sections in Quantum Chromodynamics. An ambitious goal is to link the parton shower picture with the classical radiation field.

**The student will learn:**

- what is a parton shower
- how to treat independent particle emissions within a numerical program
- in what sense can a particle ensemble be regarded as a classical field

**Requirements:**

- interest in numerical methods
- basic programming ability

Quantum Field Theory in one space-time dimension: the anharmonic oscillator and path integrals

Quantum Field Theory (QFT) in one space-time dimension is simply Quantum Mechanics (QM). It turns out that the basic model of QFT, interacting massive real scalar field theory, becomes the anharmonic oscillator once space dimensions are neglected. The main properties of the QFT system can be studied and undestood on the example of the QM model.

In this thesis, the student will use numerical path integral methods to determine the spectrum of the anharmonic oscillator, determine the presence of Spontaneous Symmetry Breaking, calculated vacuum tunneling amplitudes etc. As an outlook, it might be possible to increase the dimension of space-time and simulate QFT properties.

**The student will learn:**

- the path integral formulation of Quantum Mechanics
- numerical simulation methods for path integrals in imaginary time
- physics of Spontaneous Symmetry Breaking

**Requirements:**

- understanding of Quantum Mechanics
- basic programming ability