Theory of the Interactions with Higher Derivatives and its Application to the Non-local Interaction

Abstract

Extending Yang-Feldman's method to the system with the interaction Lagrangian with higher derivatives, we obtain the Hamiltonian in the interaction representation. Secondly, we clarify that the Hamiltonian thus obtained is nothing else than one given by usual Heisenberg-Pauli's method using the canonical conjugates differed from the independent variables of the variation, that is, if we take such canonical variables, the system is reduced to the familiar case without higher time derivatives. We can apply this theory to the non-local interaction straightfowardly and then explain the differences between the non-local interaction and the non-localized action. Also we discuss the possibilities of the removals of the divergences by introducing the non-localities.