Unified prescription for the generation of electroweak and gravitational gauge field Lagrangian on a principal fiber bundle

TL;DR

This paper presents a unified geometric framework for deriving both electroweak and gravitational gauge field Lagrangians using principal fiber bundles, highlighting the role of symmetry breaking and bundle reduction.

Contribution

It introduces a unified approach to derive electroweak and gravitational Lagrangians from Yang-Mills Weil forms on principal fiber bundles, emphasizing the geometric role of symmetry breaking.

Findings

Unified geometric derivation of electroweak and gravitational Lagrangians.

Identification of symmetry breaking as a common geometric process.

Connection between bundle reduction and physical symmetry breaking.

Abstract

The Glashow-Weinberg-Salam gauge field Lagrangian for electroweak theory and the Townsend-Zardecki action for gravitation are obtained from the same type of Yang-Mills Weil form on a principal fiber bundle over space-time, with symmetry group U(2) and SO(2,3), respectively. The unified geometrical approach given here shows that fiber bundle reduction and symmetry breaking are essential not only in electroweak theory but also in the SO(2,3) gauge theory for gravitation. In fact, the process of symmetry breaking in electroweak theory and the soldering of the anti-de Sitter bundle, essential in the interpretation of SO(2,3) gauge theory as a theory for gravitation, are corresponding geometrical concepts.