Composite Particles in Many-Body Theory

S. M. Singh

M. Popović‐Božić

Wesley E. Brittin

Cheng-Li Wu, D.H. Feng

Based on the composite particle representation presented in the last paper (I), a method of solving the many-body problem known as the composite particle approximation is proposed. It is shown that a many-body system can be simplified to a composite particle system (plus one or more uncorrelated basic particles if any existed) if the following conditions are satisfied: 1) the binding energies of the composite particles are much larger than the excitation energies of the system; 2) there is domination of the collective mode for the composite particles. The interactions between the composite particles, as well as the interactions between composite particles and the basic particles can be evaluated from the original particle-particle interactions. Applications of this theory are indicated.

Wesley E. Brittin, A.Y. Sakakura

A new fundamental theory of composite particles in nonrelativistic many-body systems is developed. The theory is constructed making use solely of the physical Fock space for the basic elementary particles which comprise the many-body system. In this manner exchange symmetry in the elementary particles is exact. Physical composite particle creation and annihilation operators are introduced and these operators satisfy exact Bose (Fermi) commutation (anticommutati$\stackrel{\mathrm{\ifmmode \dot{}\else \.{}\fi{}}}{\mathrm{o}}$n) relations depending on whether the composites correspond to bosons or to fermions. Commuting physical occupation number operators for composite particles are then constructed in the usual manner from the composite creation and annihilation operators. These number operators are highly dressed in terms of the basic elementary particle operators. Finally, the foundations of statistical mechanics for bound composite particles are formulated in terms of the appropriate occupation number operators.

Monique Combescot, Odile Betbeder-Matibet, François Dubin