Dimensional Regularization of Renyi's Statistical Mechanics

Abstract

We show that typical Renyi's statistical mechanics' quantifiers exhibit poles. We are referring to the partition function $\mathcal{Z}$ and the mean energy $<\mathcal{U}>$. Renyi's entropy is characterized by a real parameter $\alpha$. The poles emerge in a numerable set of rational numbers belonging to the $\alpha -$line. Physical effects of these poles are studied by appeal to dimensional regularization, as usual. Interesting effects are found, as for instance, gravitational ones.

22 pages, 3 figures. Text has changed. References added

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