Ciro Santilli
🔗
🔗
Originally it was likely created to study constrained mechanical systems where you want to use some "custom convenient" variables to parametrize things instead of x, y, z. Classical examples include:
🔗
However, people later noticed that the Lagrangian had some nice properties related to Lie group continuous symmetries.
🔗
Basically it seems that the easiest way to come up with new quantum field theory models is to first find the Lagrangian, and then derive the equations of motion from them.
🔗
For every continuous symmetry in the system (modelled by a Lie group), there is a corresponding conservation law.
🔗
Furthermore, given the symmetry, we can calculate the derived conservation law, and vice versa.
🔗
And partly due to the above observations, it was noticed that the easiest way to describe the fundamental laws of particle physics and make calculations with them is to first formulate their Lagrangian somehow: why do symmetries such as SU(3), SU(2) and U(1) matter in particle physics?.
🔗
🔗
Bibliography:
🔗
Video 96. "Euler-Lagrange equation explained intuitively - Lagrangian Mechanics" by Physics Videos by Eugene Khutoryansky (2018) Source. Well, unsurprisingly, it is exactly what you can expect from an Eugene Khutoryansky video.
🔗
🔗

Ancestors

🔗