Justification for zeta function regularization
Mesoscale and Nanoscale Physics
2021-09-29 v1
Abstract
Using the fact that a finite sum of power series are given by the difference between two zeta functions, we justify the usage of the zeta function with a negative variable in physical problems to avoid the divergence of the infinite sum. We will show that in the case of magnetization of graphene, the zeta function with negative variable arises as a result of cut-off energy between two consecutive Landau levels. Furthermore, similar justification can be applied to the case of zero temperature Casimir force in parallel-plate geometry.
Cite
@article{arxiv.2109.13451,
title = {Justification for zeta function regularization},
author = {F. R. Pratama and M. Shoufie Ukhtary and Riichiro Saito},
journal= {arXiv preprint arXiv:2109.13451},
year = {2021}
}
Comments
14 pages (including Supplemental material), 2 figures