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

Zeta-nonlocal scalar fields

B. G. Dragovich

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

DOI: https://doi.org/10.4213/tmf6285

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

Bibliographic databases:

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
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• http://mi.mathnet.ru/eng/tmf6285
• https://doi.org/10.4213/tmf6285
• http://mi.mathnet.ru/eng/tmf/v157/i3/p364

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
2. Dragovich B., “Towards effective Lagrangians for adelic strings”, Fortschr. Phys., 57:5-7 (2009), 546–551
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.
4. B. G. Dragovich, “The $p$-adic sector of the adelic string”, Theoret. and Math. Phys., 163:3 (2010), 768–773
5. B. G. Dragovich, “Nonlocal dynamics of $p$-adic strings”, Theoret. and Math. Phys., 164:3 (2010), 1151–1155
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
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
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
9. Górka P., Prado H., Reyes E.G., “Nonlinear Equations with Infinitely many Derivatives”, Complex Anal. Oper. Theory, 5:1 (2011), 313–323
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
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
12. Biswas T., Kapusta J.I., Reddy A., “Thermodynamics of String Field Theory Motivated Nonlocal Models”, J. High Energy Phys., 2012, no. 12, 008
13. Koshelev A.S., “Stable Analytic Bounce in Non-Local Einstein-Gauss-Bonnet Cosmology”, Class. Quantum Gravity, 30:15 (2013), 155001
14. Gorka P., Prado H., Reyes E.G., “On a General Class of Nonlocal Equations”, Ann. Henri Poincare, 14:4 (2013), 947–966
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
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
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
18. Chavez A., Prado H., Reyes E.G., “The Laplace Transform and Nonlocal Field Equations”, AIP Conference Proceedings, 2075, eds. Mishonov T., Varonov A., Amer Inst Physics, 2019, 090027-1
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