Lieb-Thirring inequalities for wave functions vanishing on the diagonal set

TL;DR

This paper develops a general method to derive Lieb-Thirring inequalities for quantum many-body systems and applies it to wave functions that vanish on the diagonal, broadening the scope of these inequalities without relying on particle statistics.

Contribution

It introduces a new strategy for deriving Lieb-Thirring inequalities applicable to scale-covariant systems and extends these inequalities to wave functions vanishing on the diagonal set.

Findings

Generalized Lieb-Thirring inequality for wave functions vanishing on the diagonal

Applicable to scale-covariant quantum many-body systems

No statistical assumptions on particles required

Abstract

We propose a general strategy to derive Lieb-Thirring inequalities for scale-covariant quantum many-body systems. As an application, we obtain a generalization of the Lieb-Thirring inequality to wave functions vanishing on the diagonal set of the configuration space, without any statistical assumption on the particles.