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Tr. Mat. Inst. Steklova, 2000, Volume 228, Pages 76–89 (Mi tm492)  

This article is cited in 7 scientific papers (total in 9 papers)

Adelic Formulas for Gamma and Beta Functions of One-Class Quadratic Fields: Applications to 4-Particle Scattering String Amplitudes

V. S. Vladimirov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Regularized adelic formulas for gamma and beta functions for arbitrary quasicharacters (either ramified or not) and in an arbitrary field of algebraic numbers are concretized as applied to one-class quadratic fields (and to the field of rational numbers). Applications to 4-tachyon tree string amplitudes, to the Veneziano (open strings) and Virasoro (closed strings) amplitudes as well as to massless 4-particle amplitudes of the Ramond–Neveu–Schwarz superstring and a heterotic string are discussed. Certain relations between different superstring amplitudes are established.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2000, 228, 67–80

Bibliographic databases:

Document Type: Article
Received in September 1999

Citation: V. S. Vladimirov, “Adelic Formulas for Gamma and Beta Functions of One-Class Quadratic Fields: Applications to 4-Particle Scattering String Amplitudes”, Problems of the modern mathematical physics, Collection of papers dedicated to the 90th anniversary of academician Nikolai Nikolaevich Bogolyubov, Tr. Mat. Inst. Steklova, 228, Nauka, MAIK Nauka/Inteperiodika, M., 2000, 76–89; Proc. Steklov Inst. Math., 228 (2000), 67–80

Citation in format AMSBIB
\Bibitem{Vla00}
\by V.~S.~Vladimirov
\paper Adelic Formulas for Gamma and Beta Functions of One-Class Quadratic Fields: Applications to 4-Particle Scattering String Amplitudes
\inbook Problems of the modern mathematical physics
\bookinfo Collection of papers dedicated to the 90th anniversary of academician Nikolai Nikolaevich Bogolyubov
\serial Tr. Mat. Inst. Steklova
\yr 2000
\vol 228
\pages 76--89
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm492}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1782573}
\zmath{https://zbmath.org/?q=an:0993.11061}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2000
\vol 228
\pages 67--80


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Dragovich B., Volovich I.V., “p-Adic strings and noncommutativity”, Noncommutative Structures in Mathematics and Physics, NATO Science Series, Series II: Mathematics, Physics and Chemistry, 22, 2001, 391–399  crossref  mathscinet  zmath  isi
    2. V. S. Vladimirov, “Beta functions of local fields of characteristic zero. Applications to string amplitudes”, Izv. Math., 66:1 (2002), 41–57  mathnet  crossref  crossref  mathscinet  zmath  elib
    3. 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
    4. M. K. Kerimov, “Vasiliĭ Sergeevich Vladimirov (on the occasion of his eightieth birthday)”, Comput. Math. Math. Phys., 43:11 (2003), 1541–1549  mathnet  mathscinet
    5. 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
    6. Dragovich B., “Non-archimedean geometry and physics on adelic spaces”, Proceedings of the Workshop on Contemporary Geometry and Related Topics, 2004, 141–158  crossref  mathscinet  zmath  isi
    7. Aref'eva, IY, “Quantization of the Riemann zeta-function and cosmology”, International Journal of Geometric Methods in Modern Physics, 4:5 (2007), 881  crossref  mathscinet  zmath  isi
    8. 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
    9. A. Yu. Khrennikov, B. Nilsson, S. Nordebo, “Quantum rule for detection probability from Brownian motion in the space of classical fields”, Theoret. and Math. Phys., 174:2 (2013), 298–306  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
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