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Quantum electrodynamics (QED) is the most accurate of all experimentallyverified physical theories. How QED and other theories of fundamentalinteractions couple to gravity through special unitary symmetries, on which thestandard model of particle physics is based, is, however, still unknown. Herewe develop a new kind of coupling between the electromagnetic field, Diracelectron-positron field, and the gravitational field based on aneight-component spinorial representation of the electromagnetic field. Ourspinorial representation is analogous to the well-known representation ofparticles in the Dirac theory but it is given in terms of 8x8 bosonic gammamatrices. In distinction to earlier works on the spinorial representations ofthe electromagnetic field, we reformulate QED using eight-component spinors.This enables us to introduce the generating Lagrangian density of gravity basedon the special unitary symmetry of the eight-dimensional spinor space. Thegenerating Lagrangian density of gravity plays, in the definition of the gaugetheory of gravity and its symmetric stress-energy-momentum tensor source term,a similar role as the conventional Lagrangian density of the free Dirac fieldplays in the definition of the gauge theory of QED and its electricfour-current density source term. The fundamental consequence, the Yang-Millsgauge theory of unified gravity, is studied in a separate work[arXiv:2310.01460], where the theory is also extended to cover the otherfundamental interactions of the standard model. We devote ample space fordetails of the eight-spinor QED to provide solid mathematical basis for thepresent work and the related work on the Yang-Mills gauge theory of unifiedgravity.

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