One-loop effective action and the Riemann Zeros
Mathematical Physics
2015-06-19 v2 High Energy Physics - Theory
math.MP
Abstract
We present a remarkable connection between the asymptotic behavior of the Riemann zeros and one-loop effective action in Euclidean scalar field theory. We show that in a two-dimensional space, the asymptotic behavior of the Fourier transform of two-point correlation functions fits the asymptotic distribution of the non-trivial zeros of the Riemann zeta function. We work out an explicit example, namely the non-linear sigma model in the leading order in expansion.
Cite
@article{arxiv.1405.6458,
title = {One-loop effective action and the Riemann Zeros},
author = {J. G. Dueñas and N. F. Svaiter and G. Menezes},
journal= {arXiv preprint arXiv:1405.6458},
year = {2015}
}