On the Discrete Spectrum of a Pseudo-Relativistic Two-Body Pair Operator

TL;DR

This paper establishes bounds and asymptotic formulas for the discrete spectrum of a pseudo-relativistic two-body operator, advancing understanding of its spectral properties in the relativistic limit.

Contribution

It provides new spectral bounds and asymptotic calculations for a two-body pseudo-relativistic operator, extending classical spectral theory results.

Findings

Derived Cwikel-Lieb-Rosenbljum bounds for the operator

Established Lieb-Thirring inequalities in the pseudo-relativistic context

Calculated spectral asymptotics for eigenvalue moments and local spectral density

Abstract

We prove Cwikel-Lieb-Rosenbljum and Lieb-Thirring type bounds on the discrete spectrum of a two-body pair operator and calculate spectral asymptotics for the eigenvalue moments and the local spectral density in the pseudo-relativistic limit.