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TMF, 2008, Volume 157, Number 3, Pages 364–372 (Mi tmf6285)  

This article is cited in 17 scientific papers (total in 17 papers)

Zeta-nonlocal scalar fields

B. G. Dragovich

University of Belgrade

Abstract: We consider some nonlocal and nonpolynomial scalar field models originating from $p$-adic string theory. An infinite number of space-time derivatives is determined by the operator-valued Riemann zeta function through the d'Alembertian $\Box$ in its argument. The construction of the corresponding Lagrangians $L$ starts with the exact Lagrangian $\mathcal L_p$ for the effective field of the $p$-adic tachyon string, which is generalized by replacing $p$ with an arbitrary natural number $n$ and then summing $\mathcal L_n$ over all $n$. We obtain several basic classical properties of these fields. In particular, we study some solutions of the equations of motion and their tachyon spectra. The field theory with Riemann zeta-function dynamics is also interesting in itself.

Keywords: nonlocal field theory, $p$-adic string theory, Riemann zeta function


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English version:
Theoretical and Mathematical Physics, 2008, 157:3, 1671–1677

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Received: 25.04.2008

Citation: B. G. Dragovich, “Zeta-nonlocal scalar fields”, TMF, 157:3 (2008), 364–372; Theoret. and Math. Phys., 157:3 (2008), 1671–1677

Citation in format AMSBIB
\by B.~G.~Dragovich
\paper Zeta-nonlocal scalar fields
\jour TMF
\yr 2008
\vol 157
\issue 3
\pages 364--372
\jour Theoret. and Math. Phys.
\yr 2008
\vol 157
\issue 3
\pages 1671--1677

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    This publication is cited in the following articles:
    1. Dragovich B., “Lagrangians with Riemann zeta function”, Romanian J. Phys., 53:9-10 (2008), 1105–1110  mathscinet  zmath  isi
    2. Dragovich B., “Towards effective Lagrangians for adelic strings”, Fortschr. Phys., 57:5-7 (2009), 546–551  crossref  mathscinet  zmath  isi  elib  scopus
    3. Vernov S.Yu., “Localization of nonlocal cosmological models with quadratic potentials in the case of double roots”, Class. Quantum Grav., 27:3 (2010), 035006, 16 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    4. B. G. Dragovich, “The $p$-adic sector of the adelic string”, Theoret. and Math. Phys., 163:3 (2010), 768–773  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    5. B. G. Dragovich, “Nonlocal dynamics of $p$-adic strings”, Theoret. and Math. Phys., 164:3 (2010), 1151–1155  mathnet  crossref  crossref  adsnasa  isi
    6. Biswas T., Cembranos J.A.R., Kapusta J.I., “Thermodynamics and cosmological constant of non-local field theories from p-adic strings”, Journal of High Energy Physics, 2010, no. 10, 048  crossref  mathscinet  isi  scopus
    7. Biswas T., Koivisto T., Mazumdar A., “Towards a resolution of the cosmological singularity in non-local higher derivative theories of gravity”, J. Cosmol. Astropart. Phys., 2010, no. 11, 008  crossref  isi  scopus
    8. Dragovich B., “On p-Adic Sector of Open Scalar Strings and Zeta Field Theory”, Lie Theory and its Applications in Physics, AIP Conference Proceedings, 1243, 2010, 43–50  crossref  adsnasa  isi  scopus
    9. Górka P., Prado H., Reyes E.G., “Nonlinear Equations with Infinitely many Derivatives”, Complex Anal. Oper. Theory, 5:1 (2011), 313–323  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    10. Gorka P., Prado H., Reyes E.G., “The initial value problem for ordinary differential equations with infinitely many derivatives”, Classical Quantum Gravity, 29:6 (2012), 065017  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    11. Biswas T., Koshelev A.S., Mazumdar A., Vernov S.Yu., “Stable Bounce and Inflation in Non-Local Higher Derivative Cosmology”, J. Cosmol. Astropart. Phys., 2012, no. 8, 024  crossref  mathscinet  isi  elib  scopus
    12. Biswas T., Kapusta J.I., Reddy A., “Thermodynamics of String Field Theory Motivated Nonlocal Models”, J. High Energy Phys., 2012, no. 12, 008  crossref  mathscinet  isi  scopus
    13. Koshelev A.S., “Stable Analytic Bounce in Non-Local Einstein-Gauss-Bonnet Cosmology”, Class. Quantum Gravity, 30:15 (2013), 155001  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    14. Gorka P., Prado H., Reyes E.G., “On a General Class of Nonlocal Equations”, Ann. Henri Poincare, 14:4 (2013), 947–966  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    15. Prado H., Reyes E.G., “On Equations With Infinitely Many Derivatives: Integral Transforms and the Cauchy Problem”, 2nd International Conference on Mathematical Modeling in Physical Sciences 2013, Journal of Physics Conference Series, 490, eds. Vagenas E., Vlachos D., IOP Publishing Ltd, 2014, 012044  crossref  isi  scopus
    16. Dragovich B. Khrennikov A.Yu. Kozyrev S.V. Volovich I.V. Zelenov E.I., “P-Adic Mathematical Physics: the First 30 Years”, P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121  crossref  mathscinet  zmath  isi  scopus
    17. Aref'eva I.Ya. Djordjevic G.S. Khrennikov A.Yu. Kozyrev S.V. Rakic Z. Volovich I.V., “P-Adic Mathematical Physics and B. Dragovich Research”, P-Adic Numbers Ultrametric Anal. Appl., 9:1 (2017), 82–85  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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