TWO AND THREE PARTICLE BRANCHES OF THE ESSENTIAL SPECTRUM OF A 3×3 OPERATOR MATRICES

Abstract

In the present paper, we precisely describe the location and structure of the essential spectrum of a 3×3 operator matrix A_μ,μ>0 associated to a system describing three particles in interaction, without conservation of the number of particles, in the quasi-momentum representation. Two and three-particle branches of the essential spectrum of A_μ are identified. The number of segments of the essential of A_μ is studied with respect to the parameter μ>0.