Is there a relativistic version of Hamiltonian mechanics? If so, how is it formulated (what are the main equations and the form of Hamiltonian)? Is it a common framework, if not then why?
It would be nice also to provide an example --- a simple system with its Hamiltonian.
As far as I remember, in relativistic mechanics we were only taught to use conservation laws, that is integral invariants and thus I have a vague perception of relativistic dynamics.