  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.
