I have been slowly chipping away at new chapters that I have been wanting to upload but I have finally finished writing my favourite section by far, Section 2.5 — Beyond Classical Mechanics: The Action in Relativistic and Quantum Theories.

This section goes beyond classical mechanics and delves into the role of the Lagrangian formalism in relativistic and quantum theories. It illustrates how our ideas of classical mechanics explored in previous sections (2.1 – 2.4), namely the Lagrangian framework and the action principle, extend far beyond their origins and help build the framework of relativistic electrodynamics, general relativity, and quantum field theories. It also includes a discussion of the path integral formulation of quantum mechanics, which builds a fundamental bridge between classical and quantum physics. Overall, this section gives a glimpse into how theoretical physicists approach modern physics and think about theories from first principles.