Regularization of p-adic String Amplitudes, and Multivariate Local Zeta Functions

2016/11/11 by Miriam Bocardo–Gaspar, Bocardo-Gaspar, Miriam, Hugo García‐Compeán +3
Mathematics · #11S40 (Primary) #46S10 (Secondary) #81E30 #81E99 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Physical sciences #Mathematical Physics (math-ph) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1611.03807

openalex publication_date 2016/11/11 · openalex created_date 2017/01/06 · openalex updated_date 2026/07/28

Abstract

We prove that the p-adic Koba-Nielsen type string amplitudes are bona fide integrals. We attach to these amplitudes Igusa-type integrals depending on several complex parameters and show that these integrals admit meromorphic continuations as rational functions. Then we use these functions to regularize the Koba-Nielsen amplitudes. As far as we know, there is no a similar result for the Archimedean Koba-Nielsen amplitudes. We also discuss the existence of divergencies and the connections with multivariate Igusa's local zeta functions.

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