Lagrangian

#basement

Lagrangian (symmetry), least action principle (stationary point), Lagrangian equations (second order)
1. $\overset{L e g e n d r e t r a n s f o r m a t i o n}{⟶}$ Hamiltonian
break down: singular. eg. gauge redundancy (Dirac bracket works), non-dynamical DOF
path integral
2.advantages: $L o r e n t z c o v a r i a n t$