3,658 karma · joined February 19, 2014
1. Action Principle: A lot of problems in mechanics can be boiled down to writing down the correct Lagrangian.
2. Statistical physics, this teaches you about to think in terms of "Zustandssummen" and is the starting point for deriving lots of interesting laws like black body radiation.
3. Field (Gauge) Theory, turns out you can write down and derive interesting Lagrangians for Electrodynamics, Fluid Dynamics and General Relativity as well.
3.1. Noethers Theorem and Symmetries allow you to get a unified view of conserved quantities.
4. Spinors, they are fundamental for understanding the quantum behaviour of matter
5. Path Integrals necessary to understand Feynman diagrams and Calculations in Quantum Field Theory.
6. Do the harmonic oscillator in as many different ways as possible, a lot of physics can be understood by solving the harmonic oscillator or coupled oscillators. Once you've understood why this is the case and the situations in which it isn't true, you will have understood a lot of physics.
I would recommend a depth first instead of breadth first approach. Pick something advanced that really interests you and work backwards what prerequisites you need to understand it. There are parts of classical physics that are super interesting but barely anyone learns about them anymore (I skimmed through Sommerfeld's lectures on theoretical physics once, they contain all kinds of super interesting problems with spinning billiard balls, tops and so on, this was at a time when Quantum Mechanics was in its infancy).
The truly interesting things discoveries within in the framework of quantum field theory, such as ADS/CFT, going from String Theory to low energy effective theories or the Amplituhedron. All of those have direct and immediate connections to state of the art quantum field theories.
What is done in (https://arxiv.org/pdf/1912.06462.pdf), especially the last part, where they suddenly invoke p-adic numbers in support of a very vague argument and a cartoon of Penrose's impossible triangle in a similar vague manner, won't be taken serious by most physicists, but is sufficient apparently to convince non-technical people to continue funding them. Nautil.us probably is just grateful for the free content.
So I was talking about the "what should I be regressing" and "transformation" (you can use gauge theory to adjust for inflation and changes in exchange rate in non-obvious ways) part. There is no question that having access to enough data and operational excellent are a complementary component.
In currency trading example the curvature $F$ of the gauge connection $A$ vanishes precisely, when there is no arbitrage opportunity. Now what Chern and Simons discovered is a differential form K (https://en.wikipedia.org/wiki/Chern–Simons_form), which when taken as the action S(A) of a gauge field $A$, has a corresponding field equation $F = 0$ (i.e. in the finance case = no arbitrage). In these equations time does not enter, however there are several ways in which on can incorporate time into the picture (for a naive example see also the lecture notes). Assets in this framework live in associated vector bundles of the principal bundle defining exchange rates.
My speculative assertion is that it is possible to identify "topological invariants" which can be computed by sequences of trades, i.e. parallel transport along the gauge connection and that those can have provably positive expected return. The fact that the fund is limited to a small amount of invested capital might be related to the fact that the strategies require measurements, that would have self-interactions if they were too large.
Another aspect is that as soon as a university is involved, you get lots of cheap basically black labor by gullible university students. Take https://qt.eu for example, they promise 1 billion in funding over 10 years and 5000+ researchers. That works out to 20000€ per researcher per year. A PhD student in Germany makes roughly double that, if he has a fully funded position. So this figure relies on:
- Paying people half the normal salary, but expecting them to work full time, which is common practice in European academia.
- Significant additional funds being provided by member states and universities, all the while the European Union has the leverage to call the shots on research direction and funding.