An interface between physics and number theory

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 mathematical route from an algebraic description of non-r...

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Bibliographic Details
Published in:Journal of physics. Conference series 2011-03, Vol.284 (1), p.012023-17
Main Authors: Duchamp, Gérard H E, Minh, Hoang Ngoc, Solomon, Allan I, Goodenough, Silvia
Format: Article
Language:English
Subjects:
Algebra
Byproducts
Constants
Field theory
Fields (mathematics)
Functions (mathematics)
Mathematical analysis
Number theory
Physics
Quantum field theory
Quantum statistics
Quantum theory
Relativistic effects
Relativistic theory
Statistical mechanics
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Summary: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 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 inter alia a basis for concluding that the Euler gamma constant γ may be rational.
ISSN:1742-6596
1742-6588
1742-6596
DOI:10.1088/1742-6596/284/1/012023