Product‐vector basis and occupation‐number basis in Fock space for bosons and fermions Available to Purchase

A basis of products of one‐particle vectors (symmetric or antisymmetric for bosons or fermions) is defined, and related to the occupation‐number basis in an abstract Fock space, a generalization of the wave‐mechanical configuration representation of the space of second quantization. Creation and destruction operators are simply defined in the product‐vector basis and shown to have their usual properties in occupation‐number representation. Algebraic properties of product vectors are developed and illustrated. The representation of operators in the product‐vector basis is described, together with a brief discussion of the effects on these operators of transformations from one set of one‐particle vectors to another. A simple treatment of density and reduced density operators for systems of bosons or fermions is given in the product‐vector basis. The relationship between degeneracy in the Fock‐space spectrum of an additive operator NA₁ and degeneracy in the spectrum of one‐particle operator A₁ is obtained.