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arXiv · 1011.0523

An interface between physics and number theory

Gérard Henry Edmond Duchamp·Vincel Hoang Ngoc Minh·Allan I. Solomon·Silvia Goodenough
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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 $γ$ may be rational.

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Gérard Henry Edmond Duchamp, Vincel Hoang Ngoc Minh, Allan I. Solomon, Silvia Goodenough. 2010-12-08. An interface between physics and number theory. https://doi.org/10.1088/1742-6596%2F284%2F1%2F012023

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