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Izv. RAN. Ser. Mat., 2002, Volume 66, Issue 1, Pages 43–58 (Mi izv370)  

This article is cited in 3 scientific papers (total in 5 papers)

Beta functions of local fields of characteristic zero. Applications to string amplitudes

V. S. Vladimirov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: For local fields $\mathbb K$ of characteristic zero, along with the beta function $\mathbf{B}_{\mathbb K}$ we introduce a new sequence $\mathbf{B}_{\mathbb K}^{(n)}$, $n=1,2,…$, of beta functions of $n$ complex arguments expressed in terms of a product of gamma functions $\boldsymbol{\Gamma}_{\mathbb K}$ for arbitrary characters (ramified or not). We consider applications to the 4-particle tree string and superstring amplitudes. It turns out that the tachyon string amplitudes can be expressed in terms of the well-known beta function $\mathbf{B}_{\mathbb K}=\mathbf{B}_{\mathbb K}^{(2)}$. The massless superstring amplitudes can be expressed in terms of the new beta function $\mathbf{B}'_{\mathbb K}=\mathbf{B}_{\mathbb K}^{(3)}$ for non-trivial characters. We establish that the amplitudes of all known strings and superstrings admit adelic formulae.
We give a new proof of the formula relating the 4-particle tree amplitudes for closed strings (generalized Virasoro amplitudes) to the product of two amplitudes for open strings (classical Veneziano amplitudes).

DOI: https://doi.org/10.4213/im370

Full text: PDF file (1054 kB)
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English version:
Izvestiya: Mathematics, 2002, 66:1, 41–57

Bibliographic databases:

Document Type: Article
UDC: 517.58+517.53.02
MSC: 53C80, 81T30, 35Q40, 81Q99, 46S10, 46F05, 46F10
Received: 05.10.2001

Citation: V. S. Vladimirov, “Beta functions of local fields of characteristic zero. Applications to string amplitudes”, Izv. RAN. Ser. Mat., 66:1 (2002), 43–58; Izv. Math., 66:1 (2002), 41–57

Citation in format AMSBIB
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\paper Beta functions of local fields of characteristic zero. Applications to string amplitudes
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\pages 43--58
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\transl
\jour Izv. Math.
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\crossref{https://doi.org/10.1070/IM2002v066n01ABEH000370}
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    This publication is cited in the following articles:
    1. A. A. Bolibrukh, A. A. Gonchar, I. V. Volovich, V. G. Kadyshevskii, A. A. Logunov, G. I. Marchuk, E. F. Mishchenko, S. M. Nikol'skii, S. P. Novikov, Yu. S. Osipov, L. D. Faddeev, D. V. Shirkov, “Vasilii Sergeevich Vladimirov (on his 80th birthday)”, Russian Math. Surveys, 58:1 (2003), 199–209  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. M. K. Kerimov, “Vasiliĭ Sergeevich Vladimirov (on the occasion of his eightieth birthday)”, Comput. Math. Math. Phys., 43:11 (2003), 1541–1549  mathnet  mathscinet
    3. V. S. Vladimirov, “Adelic Formulas for Four-Particle String and Superstring Tree Amplitudes in One-Class Quadratic Fields”, Proc. Steklov Inst. Math., 245 (2004), 3–21  mathnet  mathscinet  zmath
    4. 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
    5. V. S. Vladimirov, “Regularized adelic formulas for string and superstring amplitudes in one-class quadratic fields”, Theoret. and Math. Phys., 164:3 (2010), 1101–1109  mathnet  crossref  crossref  adsnasa  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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