Majorana spinors and extended Lorentz symmetry in four-dimensional theory

TL;DR

This paper explores an extended Lorentz symmetry in four-dimensional spacetime using Majorana spinors, introducing a fiber bundle framework that links 6D extended symmetry with 4D physics, and suggests potential dark matter candidates.

Contribution

It develops a novel 4D theory incorporating extended Lorentz symmetry via Majorana spinors and fiber bundles, connecting 6D symmetry with observable 4D physics and dark matter properties.

Findings

Extended Lorentz symmetry described by GL(4,M) group.

Introduction of extra complex fields as dark matter candidates.

Invariant action linking 6D fiber space with 4D spacetime.

Abstract

An extended local Lorentz symmetry in four-dimensional (4D) theory is considered. A source of this symmetry is a group of general linear transformations of four-component Majorana spinors GL(4,M) which is isomorphic to GL(4,R) and is the covering of an extended Lorentz group in a 6D Minkowski space M(3,3) including superluminal and scaling transformations. Physical space-time is assumed to be a 4D pseudo-Riemannian manifold. To connect the extended Lorentz symmetry in the M(3,3) space with the physical space-time, a fiber bundle over the 4D manifold is introduced with M(3,3) as a typical fiber. The action is constructed which is invariant with respect to both general 4D coordinate and local GL(4,M) spinor transformations. The components of the metric on the 6D fiber are expressed in terms of the 4D pseudo-Riemannian metric and two extra complex fields: 4D vector and scalar ones. These extra fields describe in the general case massive particles interacting with an extra U(1) gauge field and weakly interacting with ordinary particles, i.e. possessing properties of invisible (dark) matter.