Major difference between true bosons and "proteons"

TL;DR

This paper reveals fundamental differences between true bosons and proteons, composite particles made of two fermions, highlighting their non-bosonic nature, overcomplete bases, and unique closure relations affecting many-body physics.

Contribution

It demonstrates that proteons are not true bosons, introduces their distinct closure relation, and questions the validity of bosonization methods in many-body treatments.

Findings

Proteons are not true bosons due to their composite nature.

Proteon states form an overcomplete basis.

A unique closure relation explains lifetime and scattering rate relations.

Abstract

We call "proteons" -- from the ever-changing greek sea-god $\Pi\rho\omega\tau\epsilon\upsilon\varsigma$ -- composite particles made of two fermions. Among them, are the semiconductor excitons, but also various atoms and molecules, like the giant molecules made of two $^{40}$K or $^6$Li atoms which have recently Bose condensed. In addition to their indistinguishability, these composite particles are ``ever-changing'' in the sense that there is no way to know with which fermions they are precisely made. As direct consequences, (i) the proteons are not true bosons, (ii) the basis made with proteon states is \emph{overcomplete}. In spite of these difficulties, these proteons do have a nice closure relation, unexpected at first, \emph{different from the boson one} and which makes the bosonization procedures used up to now to treat many-body effects between composite bosons, rather questionable, due to possibly incorrect sum rules resulting from it. This closure relation in particular explains, in a neat way, the surprising factor 1/2 between the inverse lifetime and the sum of scattering rates which exists for exact excitons but not for boson excitons, as we have recently shown.