Gauge Theory of the full Lorentz Group on flat Spacetime

TL;DR

This paper develops a gauge theory framework for the full Lorentz group in flat spacetime, predicting novel monopole solutions and analyzing their properties within a renormalizable model.

Contribution

It introduces a comprehensive gauge theory of the Lorentz group, including interactions, equations of motion, conservation laws, and predicts new monopole solutions with potential vortex formations.

Findings

Prediction of Dirac-Clifford-'t Hooft-Polyakov monopoles

Monopoles are invariant under global Lorentz transformations

The theory is shown to be renormalizable

Abstract

We compute gauge theories of the Lorentz group. We discuss non-interacting, and interacting fermionic systems. The interacting system combines a local with a global Lorentz group, i.e, discusses a $SO(3,1)_{l}\times SO(3,1)_{g}$-theory. We compute the equations of motion and conservation laws for the fermionic matter current. The core of our work is the prediction of some new form of monopoles we call 'Dirac-Clifford-'t Hooft-Polyakov'-monopole. It resides in a state similar to color-flavor locking. Dirac-Clifford-'t Hooft-Polyakov-monopoles are invariant under global Lorentz transformations and are predicted to form vortices. The theory is renormalizable, since all Goldstone-Nambu modes are converted into massive vector gauge fields.