TY  - JOUR
AU  - Sanchis-Lozano, M. A.
AU  - Barbero, J. F.
AU  - Navarro-Salas, J.
PY  - 2012
DA  - 2012//
TI  - Prime Numbers, Quantum Field Theory and the Goldbach Conjecture
T2  - Int. J. Mod. Phys. A
JO  - International Journal of Modern Physics A
SP  - 1250136
EP  - 24pp
VL  - 27
IS  - 23
PB  - World Scientific Publ Co Pte Ltd
KW  - Quantum field theory
KW  - number theory
KW  - renormalization
KW  - Goldbach conjecture
AB  - 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.
SN  - 0217-751x
UR  - http://arxiv.org/abs/1201.6541
UR  - https://doi.org/10.1142/S0217751X12501369
DO  - 10.1142/S0217751X12501369
LA  - English
N1  - WOS:000308945100007
ID  - Sanchis-Lozano_etal2012
ER  -