# Bachelor Thesis With Prof. Czakon in 2021

Quantum Field Theory in two space-time dimension: spontaneous symmetry breaking and path integrals

Quantum Field Theory is a model within Quantum Mechanics with an infinite number of degrees of freedom. Once non-relativistic Quantum Mechanics is formulated with path integrals while Quantum Field theory is developed in a finite volume discrete space time, the differences between the theories are far less obvious. For instance, the anharmonic oscillator is just scalar field theory in one spacetime dimension.

In this thesis, the student will use numerical path integral methods to study a scalar field theory in two dimensions. The goal will be to demonstrate the presence of phase transitions, in particular of spontaneous symmetry breaking.

**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

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