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Adelic formulas for four-particle string and superstring tree amplitudes in one-class quadratic fields. (English. Russian original) Zbl 1172.81332
Proc. Steklov Inst. Math. 245, 3-21 (2004); translation from Tr. Mat. Inst. Steklova 245, 9-28 (2004).
Summary: 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 idéle group of the field is trivial on the subgroup of principal idéles 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.
For the entire collection see [Zbl 1087.46002].

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
11Z05 Miscellaneous applications of number theory
11R47 Other analytic theory
11R56 Adèle rings and groups
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