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Author  |
Sanchis-Lozano, M.A.; Barbero, J.F.; Navarro-Salas, J. |
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Title |
Prime Numbers, Quantum Field Theory and the Goldbach Conjecture |
Type |
Journal Article |
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Year |
2012 |
Publication |
International Journal of Modern Physics A |
Abbreviated Journal |
Int. J. Mod. Phys. A |
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Volume |
27 |
Issue |
23 |
Pages |
1250136 - 24pp |
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Keywords |
Quantum field theory; number theory; renormalization; Goldbach conjecture |
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Abstract |
Motivated by the Goldbach conjecture in number theory and the Abelian bosonization mechanism on a cylindrical two-dimensional space-time, 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)(dagger) – 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, allows 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. |
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Address |
[Sanchis-Lozano, Miguel-Angel; Navarro-Salas, Jose] Univ Valencia, Inst Fis Corpuscular IFIC, Ctr Mixto, CSIC, E-46100 Valencia, Spain, Email: Miguel.Angel.Sanchis@ific.uv.es; |
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Publisher |
World Scientific Publ Co Pte Ltd |
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Language |
English |
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Original Title |
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Series Volume |
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ISSN |
0217-751x |
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Notes |
WOS:000308945100007 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ pastor @ |
Serial |
1173 |
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