Spectrum of $\gamma$-Fluids: A Statistical Derivation

TL;DR

This paper derives the spectral distribution of massless bosonic and fermionic fluids with a specific equation of state using statistical methods, including the vacuum case, confirming previous thermodynamic results.

Contribution

It provides a new elementary statistical derivation of the spectra for $ ext{γ}$-fluids, including the vacuum limit, complementing earlier thermodynamic approaches.

Findings

Derived spectra for massless bosonic and fermionic fluids

Confirmed vacuum spectrum as a Lorentz invariant case

Validated previous thermodynamic derivations

Abstract

The spectrum of massless bosonic and fermionic fluids satisfying the equation of state $p=(\gamma-1)\rho$ is derived using elementary statistical methods. As a limiting case, the Lorentz invariant spectrum of the vacuum ($\gamma=0, p=-\rho$) is deduced. These results are in agreement with our earlier derivation for bosons using thermodynamics and semiclassical considerations.