Lagrangian = position/velocity
Hamiltonian = position/momentum, potential
You mentioned the Lagrangian is a way to get the Hamiltonian, meaning the position/velocity is a way to get the position/momentum and potential? How come?
Symmetries like U(1)? Why is it earlier in Lagrangian?
Why, there is no time in Lagrangian?
Probability can't occur in Lagrangian?