1. In text-books of mechanics, the Lagrangian formalism is first introduced and then the Hamiltonian is discussed which is followed by the discussions of the canonical transformations, the Hamilton-Jacobi and Poisson theories. A possibility of returning to the Lagrangian from the Hamiltonian formalisms is usually not considered. As far as the present author is aware, Ohnuki's text is the only exception, in which the problem of constructing the Lagrangian from the Hamiltonian is raised in connection with the canonical transformations. See Analytical Dynamics; Iwanami, Tokyo 1986. Unfortunately, the text is written in Japanese.
2. and , Variational Principles in Dynamics and Quantum Theory, Dover Publications, New York, 1968.
3. Relativistic Field Theories of Elementary Particles
4. For example, see Classical Field Theory; John Wiley & Sons, Inc., New York, 1976.
5. See and , Nagoya u. preprint DPNU-87hyphen;63, AICHI-1, KUNS 903 and references therein.