On Thursday 28th March at 12:30 a one-hour seminar was delivered by Professor Andreas Jüttner. This blog will attempt to cover some of the key insights delivered during the talk as concisely as possible.

The seminar started with the big bang. A brief history of the universe was outline, including dramatic events such as inflation, the formation of hadrons, and the appearance of cosmic microwave background radiation (CMBR).

After a short discussion of scales, the periodic table of fundamental particles was introduced – see figure 1. The four fundamental forces of nature had been introduced – these being strong force, the weak force, electromagnetic force and gravity, where there is a model to describe the first three, named the Standard Model.

The particles are grouped into family according to the forces that they interact with:

- Quarks interact with all three of the Standard Model forces
- The charged leptons, like the electron, interact with weak and electromagnetic forces
- The neutrinos only interact with the weak force

Familiar particles such as protons and neutrons were then fit into model, as particles called hadrons, by outlining their quark compositions – uud for protons, ddu for neutrons. It was briefly mentioned that there can be many more combinations – leading to a whole zoo of particles.

The assumption that particle masses are additive is so
intuitive that it is generally forgotten to be an assumption. However, in the
case of hadrons this is wholly not the case. One explanation for this was
derived from the well-known formula by Einstein E=mc^{2} – where the
extra mass can be thought of as extra energy instead. This is important as the
masses of protons and neutrons are only very slightly different, and any minor deviation
from these values could case major difference to the universe we live in.

This is one example of a challenge for the Standard Model. Other issues were highlighted – dark matter and energy, the fact that there’s more matter than anti-matter in the universe, and that general relativity is still yet to be reconciled with the Standard Model.

These challenges can be investigated in a number of ways, one of the key ways being physical experiments. The most impressive such experiment is the famous LHC collider at CERN. Here the Standard Model is tested through very high energy collisions.

The speakers research specifically focuses on the strong force due to the fact that interactions involving the force cannot be calculated using perturbation theory. This is due to the property of the strong force called asymptotic freedom. It is therefore necessary to use computer simulations to calculate meaningful properties involving quarks, such as the mass of a proton.

Quantum Chromo Dynamics (QCD) is the quantum field theory describing the strong force and the quarks. Within this theory quantities like the following are investigated.

However as previously mentioned, this theory is non-perturbative, so it must be done numerically. This is done by discretizing space.

The principle algorithm used is Markov Chain Monte Carlo, where ensembles of gauge configurations are evolved using as a probability distribution.

The problem is rephrased as one where the Hamiltonian equations of motion apply, and molecular dynamics evolution method can be implemented.

The full computational complexity of the problem was made
apparent when the speaker explained how it necessary for measurement to be
done, using matrices of the order 10^{18}. Such matrices are often
ill-conditioned and sparse. Computing the inverse of such matrices is very
difficult and requires a lot of RAM and computing time.

In order to make progress on such problems, it is important to understand the underlying physics to simplify the problem.

Work in this field requires the ability to run large simulations across many nodes of a supercomputer, using techniques such as MPI or OpenMP.

Of course, by taking a discretized and finite subset of the system, two major sources of error are introduced into the results. Unexpectedly, they can be classified into discretization errors and finite volume errors.

The talk concluded with a glimpse into the wide range of areas in physics where researchers in Southampton are using computational techniques to calculate properties of various Quantum Field Theories. This brought the speaker back to the beginning of the talk, where the early universe expansion phase (inflation) was returned to. By using QFT simulations for this period, predictions of the CMB can be made, which could be compared to experimental data.

**Posted by Catriona Gibbon and Ben Kitching-Morley**