The Energy of Charged Matter

TL;DR

This paper reviews techniques developed over 35 years for estimating the energy of charged matter, aiming to apply these methods to prove Dyson's conjecture on the energy scaling of a charged Bose gas.

Contribution

It highlights how existing energy estimation techniques can be improved and adapted to prove Dyson's 1967 conjecture for the energy of a charged Bose gas.

Findings

Techniques for estimating charged matter energy have been developed over 35 years.

These techniques have been used to establish stability and instability results.

Potential application to prove Dyson's $N^{7/5}$ law for charged Bose gases.

Abstract

In this talk I will discuss some of the techniques that have been developed over the past 35 years to estimate the energy of charged matter. These techniques have been used to solve stability of (fermionic) matter in different contexts, and to control the instability of charged bosonic matter. The final goal will be to indicate how these techniques with certain improvements can be used to prove Dyson's 1967 conjecture for the energy of a charged Bose gas--the sharp $N^{7/5}$ law.