Work update (30/06/2026):

Started the "Exercises and examples" section with 8 exercises on smooth submanifolds: 4 that are purely math to get familiar with differential geometry, and 4 more oriented on physics. I have finished correcting 3 of them, and will release them in this section whenever they are all done. Ultimately, these exercises are already a solid ground to cover completely point mechanics (newtonian and analytical).

In parallel, I have started to read and correct mistakes in the analytical mechanics notes. Next, I plan to finish the exercises and make progress on Hamilton equations and variational principle.

[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.