NUMBER OPERATORS FOR COMPOSITE-PARTICLES IN NON-RELATIVISTIC MANY-BODY THEORY

Commuting physical occupation number operators for composite particles are constructed using projection operator techniques. The composite particle occupation number operators are constructed from creation and annihilation operators of the elementary particles which make up the many-body system. They appear as positive operators in any given second quantized theory and represent observables within the framework of that theory. Bose-type composites have number operators with eigenvalues 0,1,2,..., and Fermi-type composites have number operators with eigenvalues 0,1. There does not arise here any problem having to do with exchange symmetry - exchange symmetry is exact, since the number operators act in the Fock space of the elementary particles. The composite particle number operators may be used in the construction of theories of composite particle reactions or equilibrium from a first principles standpoint. The construction used here not only establishes the existence of composite particle number operators but also provides some computational machinery which hopefully will aid in more practical applications. © 1980 American Institute of Physics.