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TMF, 1987, Volume 71, Number 3, Pages 337–340 (Mi tmf4962)  

This article is cited in 38 scientific papers (total in 38 papers)

$p$-adic space-time and string theory

I. V. Volovich


Abstract: Arguments are presented in favour of the hypothesis suggesting the $p$-adic structure of the space-time. A $p$-adic analogue of the Veneziano amplitude is suggested which makes it possible to start the construction of the theory of $p$-adic strings. The same problems are considered over Galois fields in which case the analogue of the Veneziano amplitude is the Jacobi sum expressed in terms of $l$-adic cohomologies of Fermat curves. An expression for the vertex operator of corresponding string theory is given.

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English version:
Theoretical and Mathematical Physics, 1987, 71:3, 574–576

Bibliographic databases:

Document Type: Article
Received: 16.11.1986

Citation: I. V. Volovich, “$p$-adic space-time and string theory”, TMF, 71:3 (1987), 337–340; Theoret. and Math. Phys., 71:3 (1987), 574–576

Citation in format AMSBIB
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\paper $p$-adic space-time and string theory
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\pages 337--340
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\transl
\jour Theoret. and Math. Phys.
\yr 1987
\vol 71
\issue 3
\pages 574--576
\crossref{https://doi.org/10.1007/BF01017088}
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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. V. S. Vladimirov, “Generalized functions over the field of $p$-adic numbers”, Russian Math. Surveys, 43:5 (1988), 19–64  mathnet  crossref  mathscinet  zmath  adsnasa  isi
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    3. A. Yu. Khrennikov, “Mathematical methods of non-Archimedean physics”, Russian Math. Surveys, 45:4 (1990), 87–125  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. D. R. Lebedev, A. Yu. Morozov, “$p$-adic single-loop calculations”, Theoret. and Math. Phys., 82:1 (1990), 1–6  mathnet  crossref  mathscinet  isi
    5. A. Yu. Khrennikov, “Generalized functions on a Non-Archimedean superspace”, Math. USSR-Izv., 39:3 (1992), 1209–1238  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. A. Yu. Khrennikov, “Generalized functions and Gaussian path integrals over non-archimedean function spaces”, Math. USSR-Izv., 39:1 (1992), 761–794  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. V. D. Ivashchuk, “Tensor Banach algebras of projective type. I”, Theoret. and Math. Phys., 91:1 (1992), 336–345  mathnet  crossref  mathscinet  zmath  isi
    8. V. S. Vladimirov, “Freund–Witten adelic formulae for Veneziano and Virasoro–Shapiro amplitudes”, Russian Math. Surveys, 48:6 (1993), 1–39  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. V. S. Vladimirov, “Derivation of Freund–Witten adelic formula for four-point Veneziano amplitudes”, Theoret. and Math. Phys., 94:3 (1993), 251–259  mathnet  crossref  mathscinet  zmath  isi
    10. É. Yu. Lerner, “Hierarchical Dyson model and $p$-adic conformal invariance”, Theoret. and Math. Phys., 97:2 (1993), 1259–1266  mathnet  crossref  mathscinet  zmath  isi
    11. A. Yu. Khrennikov, “$p$-Adic probability theory and its applications. The principle of statistical stabilization of frequencies”, Theoret. and Math. Phys., 97:3 (1993), 1340–1348  mathnet  crossref  mathscinet  zmath  isi
    12. S. S. Akbarov, “Smooth structure and differential operators on a locally compact group”, Izv. Math., 59:1 (1995), 1–44  mathnet  crossref  mathscinet  zmath  isi
    13. V. S. Vladimirov, “Adelic formulae for the gamma and beta functions of completions of algebraic number fields, and applications of them to string amplitudes”, Izv. Math., 60:1 (1996), 67–90  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. É. Yu. Lerner, M. D. Missarov, “Adelic Feynman amplitudes in lower orders of perturbation theory”, Theoret. and Math. Phys., 124:1 (2000), 938–949  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. N. N. Ganikhodzhaev, F. M. Mukhamedov, U. A. Rozikov, “$\mathbb {Z}$Existence of a Phase Transition for the Potts $p$-adic Model on the Set $\mathbb {Z}$”, Theoret. and Math. Phys., 130:3 (2002), 425–431  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. M. D. Missarov, R. G. Stepanov, “Combinatorial Optimization Problems in Ultrametric Spaces”, Theoret. and Math. Phys., 136:1 (2003), 1037–1047  mathnet  crossref  crossref  mathscinet  zmath  isi
    17. S. A. Albeverio, A. Yu. Khrennikov, V. M. Shelkovich, “Associative Algebras of $p$-Adic Distributions”, Proc. Steklov Inst. Math., 245 (2004), 22–33  mathnet  mathscinet  zmath
    18. M. D. Missarov, “Symmetry of the Renormalization Group in $p$-Adic Models”, Proc. Steklov Inst. Math., 245 (2004), 160–168  mathnet  mathscinet  zmath
    19. S. A. Albeverio, A. Yu. Khrennikov, V. M. Shelkovich, “Non-linear singular problems in $p$-adic analysis: associative algebras of $p$-adic distributions”, Izv. Math., 69:1 (2005), 221–263  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    20. Albeverio, S, “Harmonic analysis in the p-adic Lizorkin spaces: Fractional operators, pseudo-differential equations, p-adic wavelets, Tauberian theorems”, Journal of Fourier Analysis and Applications, 12:4 (2006), 393  crossref  mathscinet  zmath  isi
    21. S. V. Kozyrev, “Methods and Applications of Ultrametric and $p$-Adic Analysis: From Wavelet Theory to Biophysics”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), S1–S84  mathnet  crossref  crossref  zmath  isi  elib
    22. I. Ya. Aref'eva, I. V. Volovich, “The null energy condition and cosmology”, Theoret. and Math. Phys., 155:1 (2008), 503–511  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    23. B. G. Dragovich, “Zeta-nonlocal scalar fields”, Theoret. and Math. Phys., 157:3 (2008), 1671–1677  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    24. 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
    25. I. V. Volovich, “Bogoliubov equations and functional mechanics”, Theoret. and Math. Phys., 164:3 (2010), 1128–1135  mathnet  crossref  crossref  adsnasa  isi
    26. B. G. Dragovich, “Nonlocal dynamics of $p$-adic strings”, Theoret. and Math. Phys., 164:3 (2010), 1151–1155  mathnet  crossref  crossref  adsnasa  isi
    27. 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  isi
    28. V. M. Shelkovich, “$p$-adic evolution pseudo-differential equations and $p$-adic wavelets”, Izv. Math., 75:6 (2011), 1249–1278  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    29. Petrov N.N., “O kantorovykh kubakh”, Vestnik sankt-peterburgskogo universiteta. seriya 1: matematika. mekhanika. astronomiya, 2012, no. 3, 53–58  elib
    30. M. D. Missarov, “Functional Fourier transformation and renormalization group transformation in bosonic field theory models”, Theoret. and Math. Phys., 174:2 (2013), 263–272  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    31. S. V. Kozyrev, A. Yu. Khrennikov, V. M. Shelkovich, “$p$-Adic wavelets and their applications”, Proc. Steklov Inst. Math., 285 (2014), 157–196  mathnet  crossref  crossref  isi  elib  elib
    32. E. I. Zelenov, “The $p$-adic law of large numbers”, Izv. Math., 80:3 (2016), 489–499  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    33. E. I. Zelenov, “$p$-adic Brownian motion”, Izv. Math., 80:6 (2016), 1084–1093  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    34. Khrennikov A. Oleschko K. Correa Lopez Maria de Jesus, “Modeling Fluid's Dynamics with Master Equations in Ultrametric Spaces Representing the Treelike Structure of Capillary Networks”, Entropy, 18:7 (2016), 249  crossref  mathscinet  isi
    35. K. Oleschko, A. Yu. Khrennikov, “Applications of $p$-adics to geophysics: Linear and quasilinear diffusion of water-in-oil and oil-in-water emulsions”, Theoret. and Math. Phys., 190:1 (2017), 154–163  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    36. Lozada Aguilar M.A. Khrennikov A. Oleschko K. de Jesus Correa M., “Quantum Bayesian Perspective For Intelligence Reservoir Characterization, Monitoring and Management”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 375:2106 (2017), 20160398  crossref  isi
    37. Antoniouk V A. Oleschko K. Kochubei A.N. Khrennikov A.Yu., “A Stochastic P-Adic Model of the Capillary Flow in Porous Random Medium”, Physica A, 505 (2018), 763–777  crossref  isi
    38. Pourhadi E. Khrennikov A.Yu., “On the Solutions of Cauchy Problem For Two Classes of Semi-Linear Pseudo-Differential Equations Over P-Adic Field”, P-Adic Numbers Ultrametric Anal. Appl., 10:4 (2018), 322–343  crossref  mathscinet  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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