Dynamical Considerations on a New Approach to the Many-Body Problem

In Part A, a further analysis is made of the collective coordinate Lagrangian first introduced in a previous paper. This Lagrangian, which replaces the physical Lagrangian, describes a set of fictitious harmonic oscillators whose masses and frequencies are established. We accomplish this by adding a term to the physical Lagrangian which, however, does not affect the equations of motion. The analysis is carried out by two distinct methods: comparison of Lagrangians and comparison of equations of motion. Both methods yield identical results.In Part B, the difficult problem of representing the Dirac δ function by a finite number of terms is handled by the introduction of the d-function. A specific representation of this function is given, along with plausibility arguments that it satisfies the requirements of Part A. A brief analysis and summary of the manifold properties of the d-function is presented.