The generalized teleparallel structure

TL;DR

This paper introduces a unified framework combining Riemannian and symplectic structures to describe teleparallel geometry, revealing connections to fundamental gauge groups relevant to weak interactions.

Contribution

It proposes a novel description of teleparallel structures as a combination of Riemannian and symplectic geometries, linking to gauge groups of fundamental interactions.

Findings

The invariance group is the intersection of orthogonal and symplectic groups.

For 4D manifolds, the invariance group relates to the electro-weak interaction group.

The approach offers a new geometric perspective on fundamental forces.

Abstract

It is proposed to describe a teleparallel structure as a combination of a Riemannian and a symplectic structure. The correspondent invariance group is an intersection of the orthogonal and the symplectic groups. For a 4D manifold it turns to be the basic group of the electro-week interaction $U(1)\times SU(2).$