ARE THETA FUNCTIONS THE FOUNDATIONS OF PHYSICS ?

Abstract

The Jacobi theta functions are essentially rotations in a complex space and as such provide a basis for the lattices of the exceptional Lie algebras E₆;E₈ in complex 3-space and complex 4-space.In this note we will show that a choice of the nome q of the theta functions θ_E6;,θ_E8 leads to the equilateral tritangents of these lattices. Speciffcally we will find quarter period ratios of the real and complex axes. In particular E₈ is isomorphic to the binary icosahedral group shown recently to describe Elementary Particle theory and Quantum Gravity so q is fundamental to the structure of space itself.