The Mathematics of Physics
A few days ago, an article in Quanta Magazine caught my attention and that of many young physicists around the world.
In this article, the work of Dr. Cohl Furey is presented, which focuses on how Division algebras can provide a unifying structure for elementary particle physics. Her research provides an alternative way of putting together what we know so far about the fundamental physics in our universe and its relationship to pure math.
The main motivation of her research can be described as follows:
There are only four types of number systems that form an Algebra over a field, this is, it is possible to add, substract, multiply or divide any 2 numbers of a single system. These four number systems are: The Real numbers, the Complex numbers, the Quaternions and the Octonions.
The Real numbers are used everywhere in physics, the Complex numbers provide the mathematical structure for Quantum mechanics, the Quaternions underline the structure of Einstein's theory of special relativity, but it turns out (at least until now) that the Octonions are not central to any theory of physics.
Dr. Furey tries to use a combination of these 4 number system to describe the underlying structure of particle physics.
An introduction to her research in the form of short videos can be found on Youtube.
This is but one example of the mathematical nature of our universe. I cannot stop being amazed by how pure mathematics and physical intuition come together in the formulation of physical theories. This lead me personally to consider adding a minor in Mathematics to my studies.
After looking into the field, I found that in Switzerland theoretical physicists and mathematicians from all over the country collaborate together at the NCCR SwissMaP, which aims to encourage the interactions between both fields.
Member professors of SwissMap have put together a series of video lectures about a range of topics such as Geometry, Topology and Physics, Planar Statistical Physics and others, accessible to all interested people.
The lectures focus on providing a more precise mathematical description of nature. Exploring these video lectures offers the opportunity to graduate and undergraduate physics students to only complement and refresh their knowledge on the field, but also to discover a new perspective of the relationship between theoretical physics and mathematics.