Limiting Case of Modified Electroweak Model for Contracted Gauge Group

TL;DR

This paper proposes a modified Electroweak Model with spherical matter field geometry, exploring a limiting case with contracted gauge group that simplifies interactions while preserving particle masses.

Contribution

It introduces a new geometric modification of the Electroweak Model and analyzes a limiting case with contracted gauge group, simplifying interactions without changing particle masses.

Findings

W-boson fields become external in the limit model

Particle masses remain unchanged in the contracted model

Field interactions are simplified compared to the standard model

Abstract

The modification of the Electroweak Model with 3-dimensional spherical geometry in the matter fields space is suggested. The Lagrangian of this model is given by the sum of the {\it free} (without any potential term) matter fields Lagrangian and the standard gauge fields Lagrangian. The vector boson masses are generated by transformation of this Lagrangian from Cartesian coordinates to a coordinates on the sphere $S_3$. The limiting case of the bosonic part of the modified model, which corresponds to the contracted gauge group $SU(2;j)\times U(1)$ is discussed. Within framework of the limit model Z-boson and electromagnetic fields can be regarded as an external ones with respect to W-bosons fields in the sence that W-boson fields do not effect on these external fields. The masses of all particles of the Electroweak Model remain the same, but field interactions in contracted model are more simple as compared with the standard Electroweak Model.