Prime Numbers, quantum field theory and the Goldbach conjecture
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Prime Numbers, quantum field theory and the Goldbach conjecture

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Prime Numbers, quantum field theory and the Goldbach conjecture

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Sanchis Lozano, Miguel Ángel; Barbero González, J. Fernando; Navarro Salas, José Perfil
Aquest document és un/a article, creat/da en: 2012

Este documento está disponible también en : http://dx.doi.org/10.1142/S0217751X12501369
Motivated by the Goldbach conjecture in Number Theory and the abelian bosonization mechanism on a cylindrical two-dimensional spacetime we study the reconstruction of a real scalar field as a product of two real fermion (so-called prime) fields whose Fourier expansion exclusively contains prime modes. We undertake the canonical quantization of such prime fields and construct the corresponding Fock space by introducing creation operators $b_{p}^{\dag}$ --labeled by prime numbers p-- acting on the vacuum. The analysis of our model, based on the standard rules of quantum field theory and the assumption of the Riemann hypothesis, allow us to prove that the theory is not renormalizable. We also comment on the potential consequences of this result concerning the validity or breakdown of the Goldbach conjecture for large integer numbers.

    Sanchis Lozano, Miguel Angel Barbero González, J. Fernando Navarro Salas, José 2012 Prime Numbers, quantum field theory and the Goldbach conjecture International Journal of Modern Physics A 27 23 1250136-1 1250136-24
http://dx.doi.org/10.1142/S0217751X12501369
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