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 Tr. Mat. Inst. Steklova, 2004, Volume 245, Pages 9–28 (Mi tm167)

Adelic Formulas for Four-Particle String and Superstring Tree Amplitudes in One-Class Quadratic Fields

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Regularized adelic formulas for gamma and beta functions for arbitrary fields of algebraic numbers and arbitrary quasicharacters (ramified or not) are constructed under the condition that the corresponding quasicharacter of the idèle group of the field is trivial on the subgroup of principal idèles of this field. The problem of regularizing divergent infinite products for gamma and beta functions of local fields is solved. For the field of rational numbers and for the one-class quadratic fields, specific expressions for the adelic formulas are given. Applications to four-tachyon tree string amplitudes, generalized Veneziano amplitudes, Virasoro amplitudes with arbitrary perturbations, massless four-particle tree amplitudes (for open and closed superstrings), Neveu–Schwarz–Ramond superstring amplitudes, and amplitudes for four charged particles of a heterotic superstring are discussed.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2004, 245, 3–21

Bibliographic databases:

Document Type: Article
UDC: 512.625+517.58+511+53.02

Citation: V. S. Vladimirov, “Adelic Formulas for Four-Particle String and Superstring Tree Amplitudes in One-Class Quadratic Fields”, Selected topics of $p$-adic mathematical physics and analysis, Collected papers. Dedicated to the 80th birthday of academician Vasilii Sergeevich Vladimirov, Tr. Mat. Inst. Steklova, 245, Nauka, MAIK «Nauka/Inteperiodika», M., 2004, 9–28; Proc. Steklov Inst. Math., 245 (2004), 3–21

Citation in format AMSBIB
\Bibitem{Vla04} \by V.~S.~Vladimirov \paper Adelic Formulas for Four-Particle String and Superstring Tree Amplitudes in One-Class Quadratic Fields \inbook Selected topics of $p$-adic mathematical physics and analysis \bookinfo Collected papers. Dedicated to the 80th birthday of academician Vasilii Sergeevich Vladimirov \serial Tr. Mat. Inst. Steklova \yr 2004 \vol 245 \pages 9--28 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm167} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2099864} \zmath{https://zbmath.org/?q=an:1172.81332} \transl \jour Proc. Steklov Inst. Math. \yr 2004 \vol 245 \pages 3--21 

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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. Proc. Steklov Inst. Math., 245 (2004), 83–90
2. Dragovich B., “p-adic and adelic cosmology: p-adic origin of dark energy and dark matter”, p-ADIC Mathematical Physics, AIP Conference Proceedings, 826, 2006, 25–42
3. 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
4. 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
5. S. V. Kozyrev, “Ultrametricity in the theory of complex systems”, Theoret. and Math. Phys., 185:2 (2015), 1665–1677
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