Feynman's sunshine numbers

TL;DR

This paper explores the significance of Feynman's sunshine numbers, particularly zeta(3), in physics and mathematics, highlighting their appearances in quantum field theory, cosmology, and number theory, with solutions to related problems.

Contribution

It provides an accessible explanation of zeta values like zeta(3) and their connections to physics, including solutions to seven related problems.

Findings

Zeta(3) appears in quantum field theory calculations.

Zeta values relate to cosmological phenomena like sunshine and the Big Bang.

Solutions to seven problems involving zeta values are presented.

Abstract

This is an expansion of a talk for mathematics and physics students of the Manchester Grammar and Manchester High Schools. It deals with numbers such as the Riemann zeta value zeta(3)=sum_{n>0}1/n^3. Zeta values appear in the description of sunshine and of relics from the Big Bang. They also result from Feynman diagrams, which occur in the quantum field theory of fundamental particles such as photons, electrons and positrons. My talk included 7 reasonably simple problems, for which I here add solutions, with further details of their context.