Welcome to my personal website!

Here you can find information about my background, scientific notes and projects

Who am I?

My name is Rasmus Steen Kofoed Nielsen, and I am a P.h.D in physics, with specialization in high energy theory and cosmology

After graduating from HTX Roskilde in June 2015, I started my bachelors degree in physics at the University of Copenhagen, in September 2015. Below, you can see a complete list of my bachelor course work.

  • I completed my bachelors degree in 2018 in collaboration with my fellow student and friend Christian Schiøtt. The topic of our thesis was Hawking radiation from a type of (2+1) dimensional black holes, known as the BTZ black hole.

After completion of my bachelors degree, I began my master studies at The Niels Bohr Institute: University of Copenhagen, in September 2018. Below, you can see a complete list of my master course work.

  • During the first months of my masters degree, I worked on a research project concerning many-body solutions and black hole formation in Anti-de Sitter space. Unfortunatly, no new result were obtained.

In september of 2019, I began work on my master thesis. The project was focused on the breaking of super symmetry (SUSY) in the Anti-de Sitter space (AdS) / conformal field theory (CFT) correspondence.

  • I completed my masters degree in October 2020. My thesis was focused on making tests of AdS / CFT in a setup with broken SUSY. Some time was also dedicated to the study of integrability in this broken AdS / CFT setup.

After a break in 2021, I started my PhD work at the University of Bielefeld, in January 2022. I am currently still working on my PhD project, of which the subject is soft gluon effects on the topological susceptibility in thermal QCD. Among other things, this has relevance to the theory of Axions, which at the time of writing is considered a promissing dark matter candidate.

  • I recieved my PhD degree in June 2026.

My CV can be found here, and my Diplomas here.

Bachelor courses

Bachelor courses

Below, you will find a comprehensive list of all my completed bachelor courses

01

Introduction to Mathematics for Science

Use of Maple, Complex numbers, Number sequences, Continuous functions of 1 variable, Differentiability and integration of functions of 1 variable, Taylor's formula, Solving simple differential equations, Continuity of real functions of several variables, Topology on \( \mathbb{R}^n\), Differentiability of real functions of several variables, Extremum analysis for real functions of several variables, Lagrange's method, Surface and Volume integrals.

02

Linear Algebra in Science

Linear algebra focusing on solving linear systems of equations by Gaussian elimination, matrices and their arithmetic, determinants, real and complex vector spaces, linear mappings, bases for vector spaces and matrix representation of linear mappings, inner product and orthogonality, spectral theorems and hermitian forms.

03

Mechanics and Relativity Theory

Momentum and energy conservation, Dynamics and acceleration, Newton's laws and work, Lagrange formalism, The Newtonian and the special principle of relativity, The Galilei transformation and the Lorentz transformation, Relativistic kinematics including Lorentz contraction and time dialation, Space time, Relativistic mechanics, Moment of inertia, angular momentum and torque, Gravity, planetary motion and Kepler's laws, Periodic motion, harmonic oscillator and resonance, Newton's laws in accelerated coordinate systems

04

Mathematics for Physicists I

Vector analysis, gradient, divergence, rotation; Line, surface and volume integrals; Gauss, Greens and Stokes theorem. Vector analysis in Cartesian, polar and spherical coordinates. Continuum mechanical flows, Laplace fields, the continuity and Bernoulli equation. Hilbert spaces, eigen-functions, Sturm-Liouville problems, Fourier series and Fourier integrals. Dirac's Delta function and the convolution theorem.

05

Mathematics for Physicists II

The course provides an insight into complex function theory and into selected integral transformations as well as examples from physics where these are used. Topics covered in the course are: analytical functions, the Cauchy-Riemann conditions, the Cauchy theorem, the Cauchy integral theorem, power series, the residue theorem, Laplace transforms, solutions to simple ordinary and partial differential equations using the Fourier and Laplace transforms, the Helmholtz equation in spherical coordinates, and spherical functions.

06

Mathematics for Physicists III

The course builds on the compulsory mathematics content in the bachelor's program in the physical subjects and provides an introduction to the group theoretical methods used in modern theoretical physics. Key topics for the course are representation theory, tensors and Lie algebras. We work with finite groups as well as the Lie groups \(SO(N)\), \(SU(N)\), \(Sp(N)\) and their associated Lie algebras.

07

Thermodynamics

Classical (Boltzmann / Gibbs) and statistical thermodynamics. Analysis of thermodynamic process. The Equipartition theorem. Phase diagrams and phase transitions. Clausius-Clapeyron's relation. Use of thermodynamic equations. The concepts of temperature, heat, work, energy, free energy and entropy. The 1st and 2nd laws of thermodynamics. The equation of state and the concept of heat capacity. Use of thermodynamic PV diagrams. The concept of multiplicity and state sum. Statistical definition of entropy. The connection between entropy and heat.

08

Statistical Physics

An introduction to statistical methods in physics. The main examples are: Quantum statistics and entropy, Statistical physics and thermodynamics, State sums and distribution functions, Fermi and Bose gases, Phase transitions.

09

Probability Theory and Statistics

Key concepts: simultaneous, marginal and conditional probabilities, stochastic variables, distributions and transformations of stochastic variables, conditional distributions, mean and conditional mean, variance and covariance, Bernoulli, Binomial, Poisson, multinomial, geometric, even, normal, Chi-squared, Normal and Exponential distributions, The law of large numbers and the central limit value theorem, maximum-likelihood functions, Statistical models, estimating parameters of the statistical models, hypotheses testing, statistical independence and identical stochastic variables, confidence intervals, test sizes, simulation of stochastic variables and numerical maximum likelihood estimation.

10

Electromagnetism

The course is based on knowlegde from circuit theory, that the student has acquired in high school. The course consists of a theoretical and an experimental part. The theoretical part p rovides an introduction to basic electromagnetic concepts: electric charge, forces and fields, electric potential, dielectric materials, capacitance, current, resistance, electromotive force, magnetic fields, magnetic materials, and induction. Along the way, Maxwell's equations are systematically built up and eventually summarized with the introduction of the displacement term.

11

Electrodynamics and Waves

Key topics: Kirchhoff's laws, curcuit transients, alternating current, impedance, oscillator circuits, Maxwell's equations, Poynting's vector, electromagnetic waves, potential description of electrodynamics, dipole radiation, as well as electrodynamics and relativity.

12

Introduction to Numerical Analysis

Numerical analysis is a basic element when working with computer models in a wide range of applications such as fluid simulation, control of robots and various optimization problems. The student will work on understanding the numerical algorithms and methods from a theoretical angle. Ie. be able to explain the mathematical principles behind the numerical methods and be able to perform various proofs. For example proving that a method finds a solution, or how quickly a method can find a solution. In addition to the theoretical, the course will include programming and implementation of the reviewed methods from the theory.

13

Quantum Mechanics I

The course is a first introduction to quantum mechanics and emphasizes the basic ideas and methods of quantum physics at an elementary level. We start with the significance of the wave function and the Schrödinger equation with applications and examples of simple model potentials. Then the conceptual apparatus is further developed with the matrix (Dirac) notation. We conclude with a review of the hydrogen atom and the quantization of momentum and spin.

14

Quantum Mechanics II

The course builds on Quantum Mechanics I. The two courses provide a comprehensive introduction to the ideas, methods and applications of quantum mechanics and provide students with techniques for solving simple quantum mechanical problems. The course includes examples from different physical systems, where quantum mechanics plays a crucial role.

15

Condensed Matter Physics I

This course is a modern introduction to condensed matter physics. We will build upon basic concepts from quantum mechanics, electromagnetism, and statistical physics to develop an understanding of the properties of real materials and electronic devices. Some of the questions that we will address include: Why do some materials freely conduct electricity, while others are insulators? Why do metals feel cold to the touch? What holds the atoms together in a solid, and how do they arrange themselves? How does this arrangement affect the electronic and thermal properties of materials? How can we control the properties of semiconductors, and use these capabilities to create the building blocks for classical and quantum electronic devices?

16

Analytical Mechanics

The starting point of Analytical Mechanics is Newton's three laws of mechanics. We start by exploring consequences of Newtonian mechanics with constraints. One is naturally led to what is known as the Lagrangian mechanics and generalized coordinates. We then jump to a description based on both generalized coordinates and generalized momenta; the Hamiltonian formalism. This apparent doubling of degrees of freedom leads to the notion of canonical variables, upon which Quantum Mechanics is built.< Analytical Mechanics also allows us to describe systems with a continuous number of degrees of freedom, as in fluid dynamics, the description of membranes, etc. As such, its extension to Quantum Mechanics directly points towards Quantum Field Theory.

17

Mathematical Physics

Classical mechanics: Newtonian mechanic, Calculus of variations and Lagrangian mechanics, including Noether's theorem, Legendre-Fenchel transform and Hamiltonian mechanics, including Liouville's theorem. Quantum mechanics: Hilbert space theory, Operators on Hilbert space, including basic spectral theory, The quantum mechanical formalism, including the Schrödinger representation, the momentum representation, and Fourier transformation, The free particle, the harmonic oscillator and the hydrogen atom.

18

Discrete Mathematics

Logic, truth tables. Proofs and axiomatic structures, Sets and set operations on a logical foundation, The natural numbers, specifically induction proofs and Euclid's algorithm, Relations, specifically ordering and equivalence relations, Functions; surjectivity and injectivity, Counting problems, combinatorics, binomial coefficients, Permutations, cycle decomposition, cycle sign, Computation with class representatives, Composition rules, introductory group theory, Properties of the real numbers: field axioms, ordering and the supremum property, Introductory graph theory, Polynomials and their division.

19

Mathematical Modelling

The course illustrates how mathematical models have become a big part of modern life and supports important decisions in society. Examples will be taken from epidemiology (eg covid), economics, biology, physics, sociology, and everyday situations. We combine practical, theoretical, and scientific models. It happens in such a way that students aiming for high school develop a portfolio of models that can be used in teaching, while students in pure mathematics, statistics, mathematical economics, and physics develop the ability to apply mathematics in concrete real-life situations.

20

Theory of Science and Ethics for Physics

We will investigate the methods that science uses to generate new knowledge. What roles do theories, models and experiments play in the physical sciences? We will discuss how scientific knowledge, methods and technology interact with external societal values ​​of legal, ethical and political nature. We will introduce basic ethical theories and discuss what it means to conduct science in a morally sound, honest and responsible manner. We will examine and discuss how mathematics and physics interact, and how concepts such as big data influence classical conceptions of scientific cognition. Furthermore, the course will discuss the central epistemological role that probability plays in, for example, statistical physics and quantum mechanics.

21

Fundamentals of the Didactics of Science and Mathematics

The course is directed at all students at the Faculty of Science, who want a broad introction to the didactics of science and mathematics. Furthermore the course is a prerequisite of the advanced courses in the didactics of scientific disciplins. The main aim of the course is to be the mandatory study element of subject didactics, for students who wish to gain competence to teach at upper secondary level. For this reason significant emphasis is put on examples from the upper secondary school teaching subjects, especially mathematics, physics, chemistry, biology and nature geography.

Master courses

Master courses

Below, you will find a comprehensive list of all my completed master courses

01

Advanced Quantum Mechanics

The course is a graduate level in quantum mechanics with emphasis on providing the students with tools to understand the advanced courses within the quantum branch of the master program. The introductory undergraduate quantum mechanics curriculum is reviewed and expanded with emphasis on important concepts such as symmetries, approximate methods, scattering theory, and second quantization. It introduces the use of propagators and density matrices, applied to physical examples. Relativistic quantum mechanics is also introduced.

02

General Relativity and Cosmology

The purpose of this course is that the student obtains a basic understanding of general relativity and its applications. The first part of the course gives an introduction to Einstein's theory of general relativity. The second part of the course gives an introduction to its applications to planetary motion, bending of light, black holes, gravitational waves and cosmology.

03

Particle Physics and the Early Universe

Students will gain a basic knowledge of modern physical cosmology, including inflation both in the early stages of the evolution of the Universe and at the present days (Dark Energy). Students will gain skills in constructing multi-parameter models and analysis of their asymptotic behavior. Students will gain work experience with the observational data of the Planck experiment and their use to determine the parameters of the Standard Cosmological Model and the theory of inflation.

04

Elementary Particle Physics

The purpose of this course is to give the student an understanding of relativistic quantum field theory. A general introduction to Quantum Field Theory will be given, with an aim towards applications: Feynman diagrams, cross sections, decay rates, etc.

05

Quantum Field Theory

This course is an introduction to Quantum Field Theory. Emphasis is on the part of quantum field theory which is not just relativitic quantum mechanics. The path integral formulation of quantum mechanics is introduced and generalized to field theory. Perturbation theory of quantum field theory is developed, including the notation of Feynman rules and Feynman diagrams. The renormalization group is introduced. Quantum electro-dynamics (QED), the theory of electrons and photons, and quantum chromo-dynamics, the theory of quarks and gluons, are studied as examples of quantum gauge theories.

06

Modern Methods for Particle Scattering

The purpose of this course is to give the students an insight into various conceptual, theoretical, practical aspects of particle scattering computations. Various recent developments in such computations as well as in related topics will be discussed and we will see how to employ different modern techniques to simplify calculations maximally. We will also in the course explore hints of a deeper underlying structure governing the structure of amplitudes.

07

Introduction to Gauge/Gravity Duality

This course gives an introduction to the foundations and formulation of the gauge/gravity duality which is a correspondence between (supersymmetric) quantum field theories and gravity (string) theories. The course will introduce the students to the necessary background material and present the formulation of the duality.

08

Quantum Geometry

It is a generally accepted hypothesis that all physical phenomena can be described in terms of four fundamental forces: the electro-magnetic force, the weak and strong nuclear forces, and the gravitational force. Of these, the first three can be described by a unified so-called gauge theory, the standard model, whose mathematical framework is the geometric theory of principal and associated bundles, at the classical level...

Interests

Interests

Below, you can find a catalogue of my primary interests

Quantum Field Theory

The application of Quantum Mechanics to Classical Field Theories; the foundation of our modern understanding of High Energy Particle-Physics

General Relativity

The study of gravity as a 4-dimensional spacetime manifold with matter determining its geometry; the basis of modern Astro-Physics and Cosmology

Differential Geometry

The study of different kinds of manifolds, and the structures which these permit; central to General Relativity, Classical Mechanics and Lie-Groups

Quantum Gravity

The study of consistently combining Quantum Mechanics and General Relativity; String Theory, Loop Quantum Gravity and Causal Dynamical Triangulation are examples of Quantum gravity theories

String Theory

Initially the study of Quantized Relativistic Strings, as a way to produce spin-2 particles; Central to Holography and some modern approaches to Scattering Amplitudes

Holography and AdS/CFT

The idea that gravitational systems can be described by a dual theory in a lower-dimensional space; Important to the study of Quantum Gravity and Particle-Physics

My Github Project Repository

View a collection of various programs and scripts, pertaining to previous and ongoing projects.

Visit the repository
Projects

Projects

Below, you will find a curated selection of past and current projects of mine

  • All
  • Simulations
  • Notes
  • Scripts

Coupling-Coefficients for SO(5) Representations

A Mathematica script which can compute the coupling-coefficients between any two SO(5) representations

Notes on the Calculus of Variations

A set of notes introducing variational calculus, Lagrangian mechanics and Hamiltonian mechanics

Chaotic Pendulums

Employing numerical simulations: 4th order Runge Kutta integration, to study the chaotic nature of the classical double pendulum system

Wave function evolution

A program to simulate the 1-dimensional Schrödinger equation for various potenials

Morris-Thorne whormhole

Analysis of the Morris-Thorne whormhole solution of General Relativity

Many-body gravitation

A simulation for the dynamics of the four inner planets in our solar system