Spectral decomposition of an elementary 3-fermion 2-body operator

Abstract

The eigenvalues and eigenfunctions of an elementary 3-fermion 2-body operator $3P_g^2\wedge I^1\equiv A^3\sum _{1\le i<j\le 3}{P}_g^2(i,j)A^3$ acting on a 3-particle antisymmetric finite dimensional Hilbert space have been found. Here $P_g^2$ denotes the projection operator onto a 2-particle antisymmetric function $g^2$, while $A^3$ denotes the 3-particle antisymmetrizing operator. keywords: spectral decomposition of operators, fermion 2--body operators

12 pages