A proof of the Lieb-Thirring inequality via the Besicovitch covering lemma

TL;DR

This paper presents a novel proof of the Lieb-Thirring inequality for kinetic energy of orthonormal functions, combining microlocal analysis with the Besicovitch covering lemma to unify uncertainty and exclusion principles.

Contribution

It introduces a microlocal proof method for the Lieb-Thirring inequality utilizing the Besicovitch covering lemma, offering a new perspective on the inequality's foundations.

Findings

Proof of Lieb-Thirring inequality using microlocal techniques

Integration of uncertainty and exclusion principles via Besicovitch lemma

Potential for broader applications in quantum mechanics analysis

Abstract

We give a proof of the Lieb-Thirring inequality on the kinetic energy of orthonormal functions by using a microlocal technique, in which the uncertainty and exclusion principles are combined through the use of the Besicovitch covering lemma.