2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56085The spectrum of massless bosonic and fermionic fluids satisfying the equation of state $p=(γ-1)ρ$ is derived using elementary statistical methods. As a limiting case, the Lorentz invariant spectrum of the vacuum ($γ=0, p=-ρ$) is deduced. These results are in agreement with our earlier derivation for bosons using thermodynamics and semiclassical considerations.7 pages, LaTex, no figuresHigh Energy Physics - Theorytext