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

TL;DR

This paper derives the eigenvalues and eigenfunctions of a specific 3-fermion 2-body operator acting on a finite-dimensional antisymmetric Hilbert space, advancing the spectral analysis of fermionic operators.

Contribution

It provides the explicit spectral decomposition of an elementary 3-fermion 2-body operator, a novel analytical result in fermionic operator theory.

Findings

Eigenvalues and eigenfunctions explicitly derived

Spectral properties of the 3-fermion 2-body operator characterized

Advances understanding of fermionic operator spectral decomposition

Abstract

The eigenvalues and eigenfunctions of an elementary 3-fermion 2-body operator $3P^2_g\wedge I^1\equiv A^3 \sum\limits_{1\leq i < j \leq 3} P^2_g(i,j)A^3$ acting on a 3-particle antisymmetric finite dimensional Hilbert space have been found. Here $P^2_g$ 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