# Bachelor thesis with Prof. Czakon in 2018

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:

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

Requirements:

1. interest in numerical methods
2. basic programming ability

Spontaneous symmetry breaking in finite systems

Spontaneous Symmetry Breaking (SSB) occurs when the ground state of a system has lower symmetry than its Hamiltonian. Typical cases are the breaking of rotational symmetry in ferromagnets, translational symmetry in crystals and chiral symmetry in strong interactions. The breaking of symmetry is related to the occurence zero-gap (Goldstone) modes. In the case of ferromagnets, crystals, and strong interactions, these are magnons, phonons and pions respectively. Strictly speaking SSB can only occur in infinite systems, because of tunneling effects.

In this thesis, the student will model SSB with the help of a finite system. This allows to illustrate all the features without taking suspicious limits. Thus, it is possible to visualize the Goldstone modes (with a gap) and understand how tunneling leads to symmetry restoration. The problem will be solved both on paper and with the help of computer programs.

The student will learn:

1. what is spontaneous symmetry breaking
2. what are the conditions for its occurence
3. how finite systems model systems with an infinite number of degrees of freedom

Requirements:

1. understanding of Quantum Mechanics
2. basic programming ability