Successive canonical transformation in model two-body electrodynamics

The possibility is investigated of bypassing the no interaction theorum of Currie, Jordan and Sudarshan for direct action Lagrangians. Starting with the field theoretic description of a two-body electrodynamic problem, the field variable is solved for in terms of the particle variables, which paves the way to write an action-at-a-distance Hamiltonian for the problem. A suitable transformation is found which uncouples the field and the particle variables in the interaction up to order e2. It is shown that this transformation leaves the statement of Newton's 2nd law unchanged which also agrees with the standard results of electrodynamics. This allows for the identification of canonical variables for the proper action-at-a-distance problem. 19 references