Work update (15/07/2026):

Derived the least action principle after some additions and correction to the previous notes on Euler-Lagrange. Introduced the Hamiltonian formalism, phase space and Legendre transform. Then, I went back on the mathematical tools section to work on cotangent bundles, one form, metrics and symplectic geometry to have all the tools. Corrected ex. 5.

From now on, because of summer vacations and also to minimize stress I will publish only one longer update per months. The project starts to develop, new collaboration may hopefully start and the website may evolve. Feel free to contact me !

[Check the previous update and news]

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 louisphys@gmail.com. I am opened for collaborations.