Exploring Framed Gauge Theory as Basis for Physical Models

TL;DR

This paper introduces a framed gauge theory approach that incorporates frame vectors as dynamical variables, leading to a reformulation of the electroweak and standard models with potential insights into fermion generations and hierarchical mass patterns.

Contribution

It presents a novel framed gauge theoretical framework that unifies gauge fields and frame vectors, connecting particle physics models to gravitational structures and explaining fermion mass hierarchies.

Findings

Reformulation of electroweak theory with Higgs as part of framed gauge structure

Development of a framed standard model with global symmetry for fermion generations

Potential explanation for fermion mass and mixing hierarchies

Abstract

It is shown that by introducing as dynamical variables in the formulation of gauge theories the frame vectors (or vielbeins) in internal symmetry space, in addition to the standard gauge boson and matter fermion fields, one obtains: (i) for the $su(2) \times u(1)$ symmetry, the standard electroweak theory with the Higgs field thrown in as part of the framed gauge theoretical structure, (ii) for the $su(3) \times su(2) \times u(1)$ symmetry, a "framed standard model" with, apart from the Higgs field as before, a global $su(3)$ symmetry to play the role of fermion generations, plus some other properties which are shown elsewhere to give to both quarks and leptons hierarchical mass and mixing patterns similar to those experimentally observed. Besides, the "framing" of the standard model as such has brought the particle theory closer in structure to the theory of gravity where vierbeins have long figured as dynamical variables. Although most of the results have already been reported before, time and hindsight have allowed their presentation in this review to be made more transparent and succint.