Fermi-Bose Correspondence at Finite Temperature

TL;DR

This paper extends the Fermi-Bose correspondence to finite temperatures, proposing a novel approach that treats sea-displacement bosons at zero temperature while incorporating finite temperature effects into coefficients, successfully reproducing key dynamical functions.

Contribution

It introduces a new method for finite temperature Fermi-Bose correspondence by separating zero-temperature sea-displacement bosons from finite temperature effects, enabling correct dynamical function calculations.

Findings

Correctly reproduces finite temperature RPA dielectric function.

Finite temperature four-point and six-point functions are accurately derived.

The proposed method successfully generalizes the Fermi-Bose correspondence to finite temperatures.

Abstract

The correspondence between fermi-sea/bose-condensate displacements and the number-conserving product of two fermi/bose fields is generalised to finite temperatures. It is shown that the straightforward generalisation that involves making the sea-bosons participate in the thermodynamic averaging does not work out. A remedy is found which involves treating the sea-displacement bosons at zero temperature while all finite temperature effects have to be lumped into the coefficients. We also show that all the finite temperature dynamical four-point and six-point functions come out correctly as do some of the commutation rules involving the fermion/boson product that go through unscathed. It is also shown that this unusual prescription of leaving out the sea-bosons from the thermodynamic averaging does in fact reproduce the correct RPA dielectric function at finite temperature. This article is not however, critic-proof.