Work update (30/05/2026):
Reworked the pdf style, table of content display and added a new summary page template.
Wrote a 3 pages summary at the end of the pdf "newtonian mechanics". Introduced the generalized energy
(also known as hamiltonian), and started to derive least action principle.
Next: Before moving on to Hamilton equation and introduce Legendre transforms I wanted to already summarize everything I
learnt and derived. But then I realized I needed stronger understanding of differential geometry. I thus started reading
"The geometry of physics: an introduction" of T. Frankel, and will summarize this in the mathematical physics note.
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