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A Review of the Classical Canonical Ensemble Treatment of Newton's Gravitation
Flavia Pennini1,2,3, Angel Plastino2,4, Mario Rocca2,4,5
1Fac. de C. Exactas-National University La Pampa, Peru y Uruguay, Santa Rosa, La Pampa 6300, Argentina.
Abstract:
It is common lore that the canonical gravitational partition function Z associated with the classical Boltzmann-Gibbs (BG) exponential distribution cannot be built up because of mathematical pitfalls. The integral needed for writing up Z 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.
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