Covariant phase space with boundaries

During this session, it will be presented a covariant formulation of Hamiltonian formalism, making emphasis on the contributions of boundaries. First of all, the construction of the (pre-)phase space will be introduced, defining on it a symplectic form that, together with a Hamiltonian that has to be defined, allows us to find the time evolution of any function. Then, we continue making a detailed study of the possible contributions of the boundary terms appearing in the action and finish constructing the Hamiltonian corresponding to a given theory.