Equation of motion approach to the plasmon-plasmon interaction in a many-electron system

Using the Bohm-Pines hamiltonian we present a method for calculating the effective interaction between two plasmons by solving the equation of motion of a double-time retarded commutator defined to represent the propagation of two plasmons. This is achieved by using a decoupling procedure for the higher-order plasmon Green functions which is based on the conservation of frequency moments. The effective interaction between two plasmons is found to be repulsive, in contrast with the results obtained earlier.