# An interface between physics and number theory

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1 LIPN - Laboratoire d-Informatique de Paris-Nord 2 The Open University, Physics and Astronomy Department 3 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée

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 $\gamma$ may be rational.

Keywords : Hopf algebra Drinfel-d Associator polyzeta Euler-s gamma

Autor: Gérard Henry Edmond Duchamp - Vincel Hoang Ngoc Minh - Allan I. Solomon - Silvia Goodenough -

Fuente: https://hal.archives-ouvertes.fr/

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