An interface between physics and number theory
Abstract
We extend the Hopf algebra description of a simple quantum system given previously, to a more elaborate Hopf algebra, which is rich enough to encompass that related to a description of perturbative quantum field theory (pQFT). This provides a {\em mathematical} route from an algebraic description of non-relativistic, non-field theoretic quantum statistical mechanics to one of relativistic quantum field theory. Such a description necessarily involves treating the algebra of polyzeta functions, extensions of the Riemann Zeta function, since these occur naturally in pQFT. This provides a link between physics, algebra and number theory. As a by-product of this approach, we are led to indicate {\it inter alia} a basis for concluding that the Euler gamma constant may be rational.
Cite
@article{arxiv.1011.0523,
title = {An interface between physics and number theory},
author = {Gérard Henry Edmond Duchamp and Vincel Hoang Ngoc Minh and Allan I. Solomon and Silvia Goodenough},
journal= {arXiv preprint arXiv:1011.0523},
year = {2015}
}