On p-Adic Sector of Adelic String

TL;DR

This paper constructs a new Lagrangian for the p-adic sector of adelic open scalar strings, incorporating the Riemann zeta function with the d'Alembertian, advancing the theoretical framework of string field theory.

Contribution

It introduces a novel additive Lagrangian that unifies all p-adic Lagrangians and is an analytic function of the d'Alembertian, expanding the mathematical tools for string theory.

Findings

New Lagrangian derived from all p-adic Lagrangians

Lagrangian expressed as an analytic function of the d'Alembertian

Potential for deeper insights into Riemann zeta function in field theory

Abstract

We consider construction of Lagrangians which are candidates for p-adic sector of an adelic open scalar string. Such Lagrangians have their origin in Lagrangian for a single p-adic string and contain the Riemann zeta function with the d'Alembertian in its argument. In particular, we present a new Lagrangian obtained by an additive approach which takes into account all p-adic Lagrangians. The very attractive feature of this new Lagrangian is that it is an analytic function of the d'Alembertian. Investigation of the field theory with Riemann zeta function is interesting in itself as well.