Topological origin of vector boson masses in Electroweak Model

TL;DR

This paper proposes a topological approach to generate vector boson masses in the Electroweak Model without the Higgs field, using the transformation of matter fields from a noncompact to a compact space, linking mass generation to geometry.

Contribution

It introduces a topological mechanism for vector boson mass generation in the Electroweak Model that eliminates the need for the Higgs field, based on the curvature of matter fields space.

Findings

Vector boson masses are derived from topological transformation.

The model reproduces observed W and Z boson masses.

It interprets the parameter R as the curvature radius of matter fields space.

Abstract

The topological mechanism for generation of vector boson masses in the Electroweak Model is discussed. Vector boson masses are automatically generated by transformation of the free Lagrangian from the noncompact $R_4$ matter fields space to the compact sphere $ S_3$. This model describes all experimentally observed fields and does not include the (up to now unobserved) scalar Higgs field. $W$- and $Z$-boson masses are expressed through the parameter $R$ by the same formulas as in the standard case. The free parameter $R$ of the model is now interpreted as the curvature radius of the spherical matter fields space. The development of this topological idea in different aspects, such as transformation to radial coordinates or nonlinearly realized gauge group or nonlinear partial-trace sigma-model, is briefly reviewed.