First-order Lagrangians and the Hamiltonian formalism

We consider the problem of constructing a general unconstrained Hamiltonian formalism for a system with a finite number of degrees of freedom, starting from a general first-order Lagrangian. This construction, which uses only elements of linear algebra and the theory of partial differential equations, is given in a rather explicit form. An application of the formalism to the quantization of two-dimensional real self-dual fields is given. ((orig.))