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RESEARCH PRODUCT
PRIME NUMBERS, QUANTUM FIELD THEORY AND THE GOLDBACH CONJECTURE
Miguel-angel Sanchis-lozanoJ. Fernando Barbero G.José Navarro-salassubject
High Energy Physics - TheoryPhysicsNuclear and High Energy PhysicsPure mathematicsMathematics - Number TheoryCanonical quantizationPrime numberFOS: Physical sciencesFísicaAstronomy and AstrophysicsMathematical Physics (math-ph)Atomic and Molecular Physics and OpticsPrime (order theory)Riemann hypothesissymbols.namesakeNumber theoryHigh Energy Physics - Theory (hep-th)Goldbach's conjectureFOS: MathematicssymbolsNumber Theory (math.NT)Quantum field theoryScalar fieldMathematical Physicsdescription
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 \textit{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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-01-01 | International Journal of Modern Physics A |