Zeta Nonlocal Scalar Fields

TL;DR

This paper introduces zeta nonlocal scalar field models derived from p-adic string theory, involving an operator-valued Riemann zeta function, and explores their classical properties, solutions, and spectra.

Contribution

It constructs a novel class of scalar field models using the Riemann zeta function, extending p-adic string theory frameworks and analyzing their classical dynamics.

Findings

Derived classical solutions for zeta scalar fields

Analyzed tachyon spectra of the models

Established basic properties of the zeta nonlocal fields

Abstract

We consider some nonlocal and nonpolynomial scalar field models originated from p-adic string theory. Infinite number of spacetime derivatives is determined by the operator valued Riemann zeta function through d'Alembertian $\Box$ in its argument. Construction of the corresponding Lagrangians L starts with the exact Lagrangian $\mathcal{L}_p$ for effective field of p-adic tachyon string, which is generalized replacing p by arbitrary natural number n and then taken a sum of $\mathcal{L}_n$ over all n. The corresponding new objects we call zeta scalar strings. Some basic classical field properties of these fields are obtained and presented in this paper. In particular, some solutions of the equations of motion and their tachyon spectra are studied. Field theory with Riemann zeta function dynamics is interesting in its own right as well.