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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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ISSN |
0217-751x |
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Conference |
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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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Author |
Pla, S.; Newsome, I.M.; Link, R.S.; Anderson, P.R.; Navarro-Salas, J. |
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Title |
Pair production due to an electric field in 1+1 dimensions and the validity of the semiclassical approximation |
Type |
Journal Article |
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Year |
2021 |
Publication |
Physical Review D |
Abbreviated Journal |
Phys. Rev. D |
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Volume |
103 |
Issue |
10 |
Pages |
105003 - 23pp |
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Abstract |
Solutions to the backreaction equation in 1 + 1-dimensional semiclassical electrodynamics are obtained and analyzed when considering a time-varying homogeneous electric field initially generated by a classical electric current, coupled to either a quantized scalar field or a quantized spin-1/2 field. Particle production by way of the Schwinger effect leads to backreaction effects that modulate the electric field strength. Details of the particle production process are investigated along with the transfer of energy between the electric field and the particles. The validity of the semiclassical approximation is also investigated using a criterion previously implemented for chaotic inflation and, in an earlier form, semiclassical gravity. The criterion states that the semiclassical approximation will break down if any linearized gauge-invariant quantity constructed from solutions to the linear response equation, with finite nonsingular data, grows rapidly for some period of time. Approximations to homogeneous solutions of the linear response equation are computed and it is found that the criterion is violated when the maximum value, E-max, obtained by the electric field is of the order of the critical scale for the Schwinger effect, E-max similar to E-crit m(2)/q, where m is the mass of the quantized field and q is its electric charge. For these approximate solutions the criterion appears to be satisfied in the extreme limits qE(max)/m(2) << 1 and qE(max)/m(2) >> 1. |
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Address |
[Pla, Silvia; Navarro-Salas, Jose] Univ Valencia, Ctr Mixto Univ Valencia, Fac Fis, CSIC,Dept Fis Teor, E-46100 Valencia, Spain, Email: silvia.pla@uv.es; |
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Corporate Author |
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Publisher |
Amer Physical Soc |
Place of Publication |
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English |
Summary Language |
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ISSN |
2470-0010 |
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Conference |
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Notes |
WOS:000655874700008 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4844 |
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Author |
Navarro-Salas, J.; Pla, S. |
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Title |
(F, G)-summed form of the QED effective action |
Type |
Journal Article |
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Year |
2021 |
Publication |
Physical Review D |
Abbreviated Journal |
Phys. Rev. D |
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Volume |
103 |
Issue |
8 |
Pages |
L081702 - 7pp |
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Keywords |
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Abstract |
We conjecture that the proper-time series expansion of the one-loop effective Lagrangian of quantum electrodynamics can be summed in all terms containing the field-strength invariants F = 1/4F F-mu nu(mu nu) (x), G = 1/4 (F) over tilde F-mu nu(mu nu) (x), including those also possessing derivatives of the electromagnetic field strength. This partial resummation is exactly encapsulated in a factor with the same form as the Heisenberg-Euler Lagrangian density, except that now the electric and magnetic fields can depend arbitrarily on spacetime coordinates. We provide strong evidence for this conjecture, which is proved to sixth order in the proper time. Furthermore, and as a byproduct, we generate some solvable electromagnetic backgrounds. We also discuss the implications for a generalization of the Schwinger formula for pair production induced by nonconstant electric fields. Finally, we briefly outline the extension of these results in the presence of gravity. |
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Address |
[Navarro-Salas, Jose; Pla, Silvia] Univ Valencia, Dept Fis Teor, Valencia 46100, Spain, Email: jnavarro@ific.uv.es; |
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Publisher |
Amer Physical Soc |
Place of Publication |
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Language |
English |
Summary Language |
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Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
2470-0010 |
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Area |
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Expedition |
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Conference |
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Notes |
WOS:000649081100005 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ pastor @ |
Serial |
4834 |
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Author |
Navarro-Salas, J.; Pla, S. |
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Title |
Particle Creation and the Schwinger Model |
Type |
Journal Article |
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Year |
2022 |
Publication |
Symmetry-Basel |
Abbreviated Journal |
Symmetry-Basel |
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Volume |
14 |
Issue |
11 |
Pages |
2435 - 9pp |
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Keywords |
Schwinger model; semiclassical theory; particle creation |
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Abstract |
We study the particle creation process in the Schwinger model coupled with an external classical source. One can approach the problem by taking advantage of the fact that the full quantized model is solvable and equivalent to a (massive) gauge field with a non-local effective action. Alternatively, one can also face the problem by following the standard semiclassical route. This means quantizing the massless Dirac field and considering the electromagnetic field as a classical background. We evaluate the energy created by a generic, homogeneous, and time-dependent source. The results match exactly in both approaches. This proves in a very direct and economical way the validity of the semiclassical approach for the (massless) Schwinger model, in agreement with a previous analysis based on the linear response equation. Our discussion suggests that a similar analysis for the massive Schwinger model could be used as a non-trivial laboratory to confront a fully quantized solvable model with its semiclassical approximation, therefore mimicking the long-standing confrontation of quantum gravity with quantum field theory in curved spacetime. |
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Address |
[Navarro-Salas, Jose] Univ Valencia, Ctr Mixto Univ Valencia CSIC, Fac Fis, Dept Fis Teor & IFIC, Burjassot 46100, Valencia, Spain, Email: jnavarro@ific.uv.es |
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Corporate Author |
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Thesis |
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Publisher |
Mdpi |
Place of Publication |
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Language |
English |
Summary Language |
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Notes |
WOS:000895122100001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
5432 |
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Author |
Navarro-Salas, J. |
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Title |
Black holes, conformal symmetry, and fundamental fields |
Type |
Journal Article |
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Year |
2024 |
Publication |
Classical and Quantum Gravity |
Abbreviated Journal |
Class. Quantum Gravity |
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Volume |
41 |
Issue |
8 |
Pages |
085003 - 14pp |
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Keywords |
black holes; horizons; singularities; conformal symmetry; quantum fields; Standard Model |
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Abstract |
Cosmic censorship protects the outside world from black hole singularities and paves the way for assigning entropy to gravity at the event horizons. We point out a tension between cosmic censorship and the quantum backreacted geometry of Schwarzschild black holes, induced by vacuum polarization and driven by the conformal anomaly. A similar tension appears for the Weyl curvature hypothesis at the Big Bang singularity. We argue that the requirement of exact conformal symmetry resolves both conflicts and has major implications for constraining the set of fundamental constituents of the Standard Model. |
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Address |
[Navarro-Salas, Jose] Univ Valencia, Dept Fis Teor, IFIC, CSIC, E-46100 Burjassot, Valencia, Spain, Email: jnavarro@ific.uv.es |
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Corporate Author |
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Thesis |
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Publisher |
IOP Publishing Ltd |
Place of Publication |
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Editor |
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Language |
English |
Summary Language |
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Original Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
0264-9381 |
ISBN |
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Medium |
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Area |
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Expedition |
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Conference |
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Notes |
WOS:001187435100001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
no |
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Call Number |
IFIC @ pastor @ |
Serial |
6029 |
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