Abstract
It is common lore that the canonical gravitational partition function associated with the classical Boltzmann-Gibbs (BG) exponential distribution cannot be built up because of mathematical pitfalls. The integral needed for writing up diverges. We review here how to avoid this pitfall and obtain a (classical) statistical mechanics of Newton’s gravitation. This is done using (1) the analytical extension treatment obtained of Gradshteyn and Rizhik and (2) the well known dimensional regularization technique.
Highlights
Common lore asserts that, in dealing with gravity, the classical Boltzmann-Gibbs (BG) probability distribution is unable to produce finite results
Common lore is not able to envision the possibility of taking care of such divergences via dimensional regularization
We look at a harmonic oscillator (HO) whose Hamiltonian reads
Summary
Flavia Pennini 1,2,3, *, Angel Plastino 2,4 , Mario Rocca 2,4,5 and Gustavo Ferri 1. Exactas-National University La Pampa, Peru y Uruguay, Santa Rosa, La Pampa 6300, Argentina. Consejo Nacional de Investigaciones Científicas y Tecnológicas, (IFLP-CCT-CONICET)-C. Departamento de Física, Universidad Católica del Norte, Av. Angamos 0610, Antofagasta 2340000, Chile. Departamento de Física, Universidad Nacional de La Plata, La Plata 1900, Argentina. Departamento de Matemática, Universidad Nacional de La Plata, La Plata 1900, Argentina
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