1998/12/29 by B. Semelin, H. J. de Vega, N. Sánchez +2 · 2 citations
Physics and Astronomy · #Cosmology and Gravitation Theories #Coupling (piping) #High-Energy Particle Collisions Research #Lambda #Mathematical physics #Physics #Quantum mechanics #Quantum, superfluid, helium dynamics #Renormalization group #astro-ph
paper · pdf · doi:10.1103/physrevd.59.125021
published as Phys.Rev. D59 (1999) 125021 · LaTex, 31 pages, 11 .ps figures
arxiv created 1998/12/29 · openalex publication_date 1999/05/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The self-gravitating thermal gas (non-relativistic particles of mass m at temperature T) is exactly equivalent to a field theory with a single scalar field \ensuremathφ(x) and exponential self-interaction. We build up perturbation theory around a space dependent stationary point \ensuremathφ0(r) in a finite size domain \ensuremathδ<~r<~R (\ensuremathδ\ensuremath≪R), which is relevant for astrophysical applications (interstellar medium, galaxy distributions). We compute the correlations of the gravitational potential (\ensuremathφ) and of the density and find that they scale; the latter scales as r^\ensuremath-2. A rich structure emerges in the two-point correlators from the \ensuremathφ fluctuations around \ensuremathφ0(r). The n-point correlators are explicitly computed to the one-loop level. The relevant effective coupling turns out to be \ensuremathλ=4\ensuremathπGm2/(TR). The renormalization group (RG) equations for the n-point correlator are derived and the RG flow for the effective coupling \ensuremathλ(\ensuremathτ), \ensuremathτ=ln(R/\ensuremathδ), explicitly obtained. A novel dependence on \ensuremathτ emerges here. \ensuremathλ(\ensuremathτ) vanishes each time \ensuremathτ approaches discrete values \ensuremathτ=\ensuremathτn=2\ensuremathπn/√(7)\ensuremath-0, n=0,1,2,… . Such RG stable behavior [\ensuremathλ(\ensuremathτ) decreasing with increasing \ensuremathτ] is here connected with low density self-similar fractal structures fitting one into another. For sizes smaller than the points \ensuremathτn, RG unstable behavior appears which we connect to the Jeans unstable behavior, growing density and fragmentation. Remarkably, we get a hierarchy of scales and Jeans lengths following the geometric progression Rn=R0 e^2\ensuremathπn/√(7)=R0[10.749087…]n. A hierarchy of this type is expected for non-spherical geometries, with a ratio different from e^2\ensuremathπ/√(7).