We study in a rigorous mathematical way p-adic quantum field theories whose N-point amplitudes are the expectation of products of vertex operators. We show that this type of amplitudes admit a series expansion where each term is an Igusa's local zeta function. The lowest term in this series is a regularized version of the p-adic open Koba-Nielsen string amplitude.
Fuquen-Tibatá, A. R., H. García-Compeán, and W. A. Zúñiga-Galindo. "Euclidean quantum field formulation of p-adic open string amplitudes." Nuclear Physics B (2022): 115684.
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Nuclear Physics B