On Lagrangian and Hamiltonian Formalism

The theory of transformation functions, as has been developed by Schwinger, Feynman, Dyson and others, is investigated systematically with mechanical models, keeping close analogy to classical theory; and a new light is thereby thrown on the relation between the Lagrangian and Hamiltonian formalism. In these investigations the idea of chronological ordering introduced by Dyson on the one hand, and a differential operation with respect to coupling constant (or some other parameters) on the other, play a decisive part. The formulation is extended to a point where dynamical systems with higher time derivatives as well as “non-local” systems (with integral equations of motion) are included.