Work update [RELEASE] (15/04/2026):

Defined what kind of physical quantities can be called conserved and introduced the concepts of state space. Derived the transport equation as a consequence, and studied what it means using these definitions for the momentum, the angular momentum and the energy to be conserved. Notes are available in the classical mechanics section.

After a short section on harmonic oscillator and periodic motions, I plan to move to analytical mechanics, Euler-Lagrange and Hamilton equations. In parallel, I plan to start an appendix dedicated on dynamical systems, phase space and Liouville theorem.

[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.