QED based on eight-dimensional spinorial wave equation of the electromagnetic field and the emergence of quantum gravity

TL;DR

This paper introduces an eight-dimensional spinorial formulation of QED that unifies electromagnetic and gravitational interactions through a novel gauge theory based on special unitary symmetry.

Contribution

It develops a new eight-component spinorial representation of the electromagnetic field, enabling a gauge theory of gravity within the QED framework, extending the standard model's symmetry principles.

Findings

Reformulation of QED using eight-component spinors.

Introduction of a gravity-generating Lagrangian density based on SU(8) symmetry.

Foundation for a Yang-Mills gauge theory of unified gravity.

Abstract

Quantum electrodynamics (QED) is the most accurate of all experimentally verified physical theories. How QED and other theories of fundamental interactions couple to gravity through special unitary symmetries, on which the standard model of particle physics is based, is, however, still unknown. Here we develop a coupling between the electromagnetic field, Dirac electron-positron field, and the gravitational field based on an eight-component spinorial representation of the electromagnetic field. Our spinorial representation is analogous to the well-known representation of particles in the Dirac theory but it is given in terms of 8x8 bosonic gamma matrices. In distinction from earlier works on the spinorial representations of the electromagnetic field, we reformulate QED using eight-component spinors. This enables us to introduce the generating Lagrangian density of gravity based on the special unitary symmetry of the eight-dimensional spinor space. The generating Lagrangian density of gravity plays, in the definition of the gauge theory of gravity and its symmetric stress-energy-momentum tensor source term, a similar role as the conventional Lagrangian density of the free Dirac field plays in the definition of the gauge theory of QED and its electric four-current density source term. The fundamental consequence, the Yang-Mills gauge theory of unified gravity, is studied in a separate work [arXiv:2310.01460], where the theory is also extended to cover the other fundamental interactions of the standard model. We devote ample space for details of the eight-spinor QED to provide solid mathematical basis for the present work and the related work on the Yang-Mills gauge theory of unified gravity.