Geodesic
On $p$-adic aspects of some perturbation series
Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 2, pp. 211-218 
B. G. Dragovich. On $p$-adic aspects of some perturbation series. Teoretičeskaâ i matematičeskaâ fizika, Tome 93 (1992) no. 2, pp. 211-218. http://geodesic.mathdoc.fr/item/TMF_1992_93_2_a1/
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     title = {On $p$-adic aspects of some perturbation series},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Series with factorial terms, which are of potential interest in quantum field theory and string theory, are considered. Divergent series in the real case are usually $p$-adic convergent. Using simple and number field invariant methods of summation, rational sums are obtained. Sums of the convergent and divergent counterparts of the same series are connected by adelic summability.

[1] Schikhof W. H., Ultrametric Calculus, Cambridge Univ. Press, 1984 | MR | Zbl

[2] Volovich I. V., Class. Quantum Grav., 4 (1987), 83 ; Grossman B., Phys. Lett. B, 197 (1987), 101 ; Freund P. G. O., Olson M., Phys. Lett. B, 199 (1987), 186 ; Freund P. G. O., Witten E., Phys. Lett. B, 199 (1987), 191 ; Frampton P. H., Okada Y., Phys. Rev. Lett., 60 (1988), 484 ; Aref'eva I. Ya., Dragović B. G., Volovich I. V., Phys. Lett. B, 209 (1988), 445 ; 212 (1988), 283 ; 214 (1988), 339 | DOI | MR | DOI | MR | Zbl | DOI | MR | DOI | MR | DOI | MR | DOI | MR | DOI | MR | DOI | MR

[3] Alacoque C., Ruelle P., Thiran E., Verstegen D., Weyers J., Phys. Lett. B, 211 (1988), 59 ; Vladimirov V. S., Volovich I. V., Commun. Math. Phys., 123 (1989), 659 ; Meurice Y., Int. J. Mod. Phys. A, 4 (1989), 5133 ; Khrennikov A. Yu., J. Math. Phys., 32 (1991), 932 | DOI | MR | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl

[4] Volovich I. V., Number theory as the ultimate physical theory, Preprint CERN-TH 4781/87, 1987 | MR

[5] Dragović B. G., Frampton P. M., Urošević B. V., Mod. Phys. Lett. A, 5 (1990), 1521 ; Aref'eva I. Ya., Dragović B. G., Frampton P. H., Volovich I. V., Int. J. Mod. Phys. A, 6 (1991), 4341 | DOI | MR | Zbl | DOI | MR | Zbl

[6] Dragović B. C., Phys. Lett. B, 256 (1991), 392 | DOI | MR

[7] Gross D. J., Periwal V., Phys. Rev. Lett., 60 (1988), 2105 | DOI | MR

[8] Koblitz N., $P$-adic Numbers, $P$-adic Analysis and Zeta-functions, Springer, Berlin, 1984 | MR

[9] Vorob'ev N. N., Teoriya ryadov, Nauka, Moscow, 1986 (Russian) | MR