We considered the canonical gravitational partition function Z associated to the classical Boltzmann–Gibbs (BG) distribution e−βHZ. It is popularly thought that it cannot be built up because the integral involved in constructing Z 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.
Neutrino oscillation parameters can be understood in a better way by building a more complete picture of neutrino interactions. This poses a series of important theoretical and experimental challenges, given the elusive nature of neutrino and an inherent difficulty in its detection. This work is an attempt to study the neutrino interactions through a purely theoretical approach using the concept of vacuum fluctuation particle pairs, where an antiparticle from a virtual particle pair is captured via annihilation, allowing the matter particle of the virtual pair to become free. Though experiments are trying hard to shed more light on neutrino interactions, our knowledge of neutrino oscillation parameters is not precise at different energy levels. In this context, one cannot help but give a bold try to marvel at how far our theoretical frameworks can extend.
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