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Gravitational effects in birefringent quantum electrodynamics

The most general classical electrodynamics which still respect the linear superposition principle but allow for otherwise arbitrary birefringence require, and imply, a refined spacetime geometry described by a fourth-rank tensor field. Canonical gravitational dynamics for this geometry, if required to co-evolve in causally consistent fashion with the electromagnetic field, were shown to be constructively determined by gravitational closure of the birefringent electromagnetic field equations. For weak gravitational fields of the resulting birefringent refinement of classical Einstein-Maxwell theory, we show in this article that the corresponding quantum electrodynamics is locally renormalizable at every loop order in gauge-invariant fashion and then employ this result to compute various fundamental processes. Combining quantum field theoretic results in locally essentially flat regions with the global spacetime structure predicted by the refined gravitational dynamics, we find that the anomalous magnetic moment of the electron, the cross sections of Bhabha scattering, and the hyperfine splitting of the hydrogen all pick up a dependence on position in the gravitational field. Particularly the measurement of the hyperfine line of hydrogen, but quite generally the measurement of any local quantum electrodynamical process, is thus able to inform the search for vacuum birefringence and its effects in a new way, since the gravitational theory allows to predict where the effects will be most pronounced.