On the Essential Spectrum of Many-Particle Pseudorelativistic Hamiltonians with Permutational Symmetry Account

TL;DR

This paper investigates the essential spectrum of many-particle pseudorelativistic Hamiltonians with various permutational symmetries, providing new insights into its location and properties relevant for spectral analysis.

Contribution

It formulates the essential spectrum for such Hamiltonians across different symmetry types and establishes new bounds for the spectrum's lower edge.

Findings

Location of the essential spectrum for all symmetry types

New properties of the lower bound of the spectrum

Results applicable to the study of discrete spectrum

Abstract

In this paper we formulate our results on the essential spectrum of many-particle pseudorelativistic Hamiltonians without magnetic and external potential fields in the spaces of functions, having arbitrary type $\alpha$ of the permutational symmetry. We discover location of the essential spectrum for all $\alpha$ and for some cases we establish new properties of the lower bound of this spectrum, which are useful for study of the discrete spectrum.