Generalized quantization formalism.

Abstract

A generalized quantization formalism (QF) is proposed which works for the partial space (e.g., the orbital, or spin, or color) space as well as for the total space. The creation and annihilation operators in the generalized QF are in general neither boson nor fermion operators. However, if we restrict ourselves to the totally antisymmetric (symmetric) states (including any intermediate states), then they are reduced to the fermion (boson) operators. Therefore, the generalized QF is an extension of the second QF. The generalized QF is superior to both the first and second QF for computing the matrix elements in a basis which has definite symmetry in each subspace. Using the generalized QF, the shell-model calculation for the multishell, multispin case is reduced to that for the single-shell, single-spin case, and the Brussaard and Glaudemans results become the trivial case of two shell and zero spin, i.e., the case (${\ensuremath{\gamma}}_{11}^{\mathit{n}}$${\ensuremath{\gamma}}_{22}^{\mathit{n}}$), where \ensuremath{\gamma}=j or jt.