Why is it possible to define an $\mathbb R$-torsor/$\mathbb R$-bundle out of the Lagrangian and to construct a projective limit? (I'm guessing this has to do with time evolution acting on the space of paths.)
Also, how is this related to conservative forces? I know that conservative forces basically allow one to define a potential that only depends on position. Is this in any way related to the boundary term in the Euler-Lagrange Eqs?
Finally, what's the relation between the boundary term and Hamiltonian mechanics, resp. the Legendre transform?
Thanks in advance.
