Classical Partition Function for Non-Relativistic Gravity

HAMEEDA, MIR; PLASTINO, ANGELO; ROCCA, MARIO CARLOS; ZAMORA, DARÍO JAVIER

Modern Problems of Mathematical Physics and Their Applications

MDPI

Lugar: Basel; Año: 2022; p. 227 - 236

We considered the canonical gravitational partition function associated to the classical Boltzmann-Gibbs (BG) distribution. It is popularly thought that it cannot be built up because the integral involved in constructing diverges at the origin. Contrariwise, it was shown in (Physica A 497 (2018) 310), by appeal to sophisticated mathematics developed in the second half of the last century, that this is not so. Z can indeed be computed by recourse to (A) the analytical extension treatments of Gradshteyn and Rizhik and Guelfand and Shilov, that permit tackling some divergent integrals and (B) the dimensional regularization approach. Only one special instance was discussed in the above reference. In this work, we obtain the classical partition function for Newton's gravity in the four cases that immediately come to mind.