Geodesic
Zeta-nonlocal scalar fields
Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 3, pp. 364-372 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     url = {http://geodesic.mathdoc.fr/item/TMF_2008_157_3_a3/}
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B. G. Dragovich. Zeta-nonlocal scalar fields. Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 3, pp. 364-372. http://geodesic.mathdoc.fr/item/TMF_2008_157_3_a3/

[1] I. V. Volovich, TMF, 71:3 (1987), 337–340 | DOI | MR | Zbl

[2] L. Brekke, P. G. O. Freund, Phys. Rep., 233:1 (1993), 1–66 | DOI | MR

[3] V. S. Vladimirov, I. V. Volovich, E. I. Zelenov, $p$-Adicheskii analiz i matematicheskaya fizika, Nauka, M., 1994 | MR | MR | Zbl

[4] L. Brekke, P. G. O. Freund, M. Olson, E. Witten, Nucl. Phys. B, 302:3 (1988), 365–402 | DOI | MR

[5] P. H. Frampton, Y. Okada, Phys. Rev. D, 37:10 (1988), 3077–3079 | DOI | MR

[6] D. Ghoshal, A. Sen, Nucl. Phys. B, 584:1–2 (2000), 300–312 ; arXiv: hep-th/0003278 | DOI | MR | Zbl

[7] J. A. Minahan, JHEP, 03 (2001), 028 ; arXiv: hep-th/0102071 | DOI | MR

[8] A. Sen, JHEP, 10 (2002), 003 ; arXiv: hep-th/0207105 | DOI | MR

[9] N. Moeller, B. Zwiebach, JHEP, 10 (2002), 034 ; arXiv: hep-th/0207107 | DOI | MR

[10] I. Ya. Aref'eva, L. V. Joukovskaya, A. S. Koshelev, JHEP, 09 (2003), 012 ; arXiv: hep-th/0301137 | DOI | MR

[11] D. Ghoshal, T. Kawano, Nucl. Phys. B, 710:3 (2005), 577–598 ; ; P. Grange, Phys. Lett. B, 616:1–2 (2005), 135–140 ; arXiv: hep-th/0409311arXiv: hep-th/0409305 | DOI | MR | Zbl | DOI | MR | Zbl

[12] B. Dragovich, I. V. Volovich, “$p$-Adic strings and noncommutativity”, Noncommutative Structures in Mathematics and Physics, NATO Sci. Ser. II, Math. Phys. Chem., 22, eds. S. Duplij, J. Wess, Kluwer, Dordrecht, 2001, 391–399 ; D. Ghoshal, JHEP, 09 (2004), 041 ; arXiv: hep-th/0406259 | MR | Zbl | DOI | MR

[13] V. S. Vladimirov, Ya. I. Volovich, TMF, 138:3 (2004), 355–368 ; arXiv: math-ph/0306018 | DOI | MR | Zbl

[14] V. S. Vladimirov, TMF, 149:3 (2006), 354–367 ; arXiv: 0705.4600 | DOI | MR | Zbl

[15] N. Barnaby, N. Kamran, Dynamics with infinitely many derivatives: the initial value problem, arXiv: 0709.3968v1 | MR

[16] I. Ya. Aref'eva, “Nonlocal string tachyon as a model for cosmological dark energy”, $p$-Adic Mathematical Physics, AIP Conf. Proc., 826, AIP, New York, 2006, 301–311 ; arXiv: astro-ph/0410443 | DOI | MR | Zbl

[17] I. Ya. Arefeva, I. V. Volovich, TMF, 155:1 (2008), 3–12 ; arXiv: hep-th/0612098 | DOI | MR | Zbl

[18] N. Barnaby, T. Biswas, J. M. Cline, JHEP, 04 (2007), 056 ; arXiv: hep-th/0612230 | DOI | MR

[19] I. Ya. Aref'eva, L. V. Joukovskaya, S. Yu. Vernov, JHEP, 07 (2007), 087 ; arXiv: hep-th/0701184 | DOI | MR

[20] G. Calcagni, M. Montobbio, G. Nardelli, Phys. Rev. D, 76:12 (2007), 126001 ; arXiv: 0705.3043 | DOI | MR

[21] D. Ghoshal, Phys. Rev. Lett., 97:15 (2006), 151601 | DOI | MR | Zbl

[22] B. G. Dragovich, TMF, 101:3 (1994), 349–359 ; Internat. J. Modern Phys. A, 10:16 (1995), 2349–2365 ; arXiv: hep-th/0404160 | DOI | MR | Zbl | DOI | MR | Zbl

[23] I. Ya. Aref'eva, I. V. Volovich, Int. J. Geom. Methods Mod. Phys., 4:5 (2007), 881–895 ; arXiv: hep-th/0701284 | DOI | MR | Zbl

[24] I. Ya. Aref'eva, B. G. Dragovich, I. V. Volovich, Phys. Lett. B, 209:4 (1988), 445–450 | DOI | MR

[25] A. Gerasimov, S. Shatashvili, JHEP, 10 (2000), 034 ; arXiv: hep-th/0009103 | DOI | MR

[26] B. Dragovich, Zeta strings, arXiv: hep-th/0703008

[27] N. Moeller, M. Schnabl, JHEP, 01 (2004), 011 ; arXiv: hep-th/0304213 | DOI | MR