Geodesic
Adelic Formulas for Four-Particle String and Superstring Tree Amplitudes in One-Class Quadratic Fields
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 9-28

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TM_2004_245_a1,
     author = {V. S. Vladimirov},
     title = {Adelic {Formulas} for {Four-Particle} {String} and {Superstring} {Tree} {Amplitudes} in {One-Class} {Quadratic} {Fields}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {9--28},
     publisher = {mathdoc},
     volume = {245},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2004_245_a1/}
}
TY  - JOUR
AU  - V. S. Vladimirov
TI  - Adelic Formulas for Four-Particle String and Superstring Tree Amplitudes in One-Class Quadratic Fields
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2004
SP  - 9
EP  - 28
VL  - 245
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2004_245_a1/
LA  - ru
ID  - TM_2004_245_a1
ER  - 
%0 Journal Article
%A V. S. Vladimirov
%T Adelic Formulas for Four-Particle String and Superstring Tree Amplitudes in One-Class Quadratic Fields
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2004
%P 9-28
%V 245
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2004_245_a1/
%G ru
%F TM_2004_245_a1
V. S. Vladimirov. Adelic Formulas for Four-Particle String and Superstring Tree Amplitudes in One-Class Quadratic Fields. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 9-28. http://geodesic.mathdoc.fr/item/TM_2004_245_a1/