Abstract :
A model problem, initially proposed by Feynman and Hibbs, is re-examined in this work. It is shown that the equation of motion is deterministic, in spite of its double time delay character, and has chaoticlike solutions. It is further shown that this model is amenable to the methods of higher than first-order Lagrangians, yielding a series of approximations to the initial model. Thus, for each approximation, a complete set of canonical variables can be defined, the Hamiltonian can be written down in canonical form and the conventional quantization rules applied, leading to exact quantizations. Extended sets of basis vectors follow along with the definition of physical state vectors, which are seen to contain all of the classical information. Finally, these results are used to give a possible explanation of the electron-position resonances seen in heavy-ion collision experiments that is consistent with the negative results found in low-energy electron scattering as well as other heavy-ion collision experiments.
