Work update (01/09/2026):
Finished the mathematical tools section: from the definition of a submanifold to metric, exterior algebra, k-forms, Stokes theorem
as well as Cartan's magic formula and cohomology. This section is a solid basis asking to be expanded, but covering a nice overview of
differential geometry for analytic mechanics.
In the meantime, I fixed many typos and mistakes in other notes, reworked the first part of analytical mechanics and keep writing corrected
exercises. I will soon publish the second part of analytical mechanics on Hamilton equation and Liouville theorem, then start statistical physics.
Welcome
Physics Compiled is a long-term personal project: a structured attempt to understand how mathematical structures emerge from (and constrain) experimental reality.
These notes are neither popular science nor a conventional textbook. They aim to pedagogically present complex physics through equations. The three general rules I follow when writing them down is:
- Pedagogy — explain concepts with clarity, especially by connecting them to facts
- Mathematical meaning — presenting the equation, without getting too far in pure mathematics (or in appendices)
- Independency — each section must be readable on its own, but can reference others.
The guiding questions are simple:
- Why was a model introduced?
- What experiments forced this structure upon us?
- Could we have made different assumptions?
The objective is ambitious: to cover most major domains of physics (from classical mechanics to quantum fields) in a unified narrative written in my own words. It comes from my desire of understanding mathematically every phenomenon that I'm looking at. In physics, equations are a language.
This is a living document. Criticism, discussion, and collaboration are warmly welcome. Feel free to create issues the github repository or directly contact me at
A dynamical system. Taken from this article