Periods and Applications

TL;DR

This paper surveys the mathematical concept of periods, their properties, and applications in physics and number theory, while also exploring their analogs in finite characteristic and connections to string theory.

Contribution

It provides a comprehensive overview of periods, including their elementary properties, examples like Feynman Integrals and Multiple Zeta Values, and discusses their analogs in finite characteristic and string theory.

Findings

Periods include Feynman Integrals and Multiple Zeta Values.

Connections between periods and Jacobi sums are discussed.

Exploration of periods in finite characteristic and string theory contexts.

Abstract

Periods are numbers represented as integrals of rational functions over algebraic domains. A survey of their elementary properties is provided. Examples of periods includes Feynman Integrals from Quantum Physics and Multiple Zeta Values from Number Theory. But what about finite characteristic, via the global-to-local principle? We include some considerations regarding periods and Jacobi sums, the analog of Veneziano amplitudes in String Theory.