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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 electronpositron field, and the gravitational field based on an eightcomponent spinorial representation of the electromagnetic field. Our spinorial representation is analogous to the wellknown representation of particles in the Dirac theory but it is given in terms of 8×8 bosonic gamma matrices. In distinction from earlier works on the spinorial representations of the electromagnetic field, we reformulate QED using eightcomponent spinors. This enables us to introduce the generating Lagrangian density of gravity based on the special unitary symmetry of the eightdimensional spinor space. The generating Lagrangian density of gravity plays, in the definition of the gauge theory of gravity and its symmetric stressenergymomentum 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 fourcurrent density source term. The fundamental consequence, the YangMills 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 eightspinor QED to provide solid mathematical basis for the present work and the related work on the YangMills gauge theory of unified gravity.
Original language  English 

Article number  032224 
Number of pages  27 
Journal  Physical Review A 
Volume  109 
Issue number  3 
DOIs  
Publication status  Published  27 Mar 2024 
MoE publication type  A1 Journal articlerefereed 
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 1 Active

OptiForce  Partanen: Unified theory of optical force fields and its engineering applications
01/09/2022 → 31/08/2025
Project: Academy of Finland: Other research funding