REPRESENTATIONS OF GENERAL COMMUTATION RELATIONS

General commutation relations involving creation, annihilation, and pa rticle number operators are considered. Such commutation relations ari se in the context of nonstandard Poisson brackets. All possible types of irreducible representations in which the particle number operator o r the product of the creation and annihilation operators has a basis o f orthonormal eigenvectors are constructed. The irreducible representa tions that involve the particle number operator reduce to one of four types and those that do not involve the particle number operator reduc e to one of five types.