Alpha and Electro-weak Coupling

TL;DR

This paper explores the mathematical relationship between the fine structure constant and group representations, proposing a geometric interpretation and a generalized Weinberg angle related to electroweak coupling.

Contribution

It introduces a novel group-theoretic framework linking the fine structure constant to cyclic group representations and generalizes the electroweak mixing angle.

Findings

Identifies a specific group-theoretic value matching the fine structure constant.

Proposes a geometric interpretation of electroweak coupling constants.

Introduces a generalized Weinberg angle based on representation geometry.

Abstract

It is shown that the fine structure constant alpha has the same value that "characterises" a relation, denoted by alpha_137(29*137), between a representation of the cyclic group of order 29*137 and the induced representation for the cyclic subgroup of order 137. The value of this characteristic is alpha_137(29*137) = 0.007297352532... . The complementary characteristic alpha_29(29*137)=0.034280626357... for the cyclic subgroup of order 29 is shown to represent the gauge theory electro-weak coupling quantity g^2/(4 pi). Kinematic aspects of the representation geometry are discussed and a generalized version of the Weinberg electro-weak mixing angle is introduced.