Gauge independent quantum gravitational corrections to Maxwell’s equation

Abstract

We consider quantum gravitational corrections to Maxwell’s equations on flat space background. Although the vacuum polarization is highly gauge dependent, we explicitly show that this gauge dependence is canceled by contributions from the source which disturbs the effective field and the observer who measures it. Our final result is a gauge independent, real and causal effective field equation that can be used in the same way as the classical Maxwell equation.

How inflationary gravitons affect gravitational radiation

“…The new technique was implemented at one loop order for quantum gravitational corrections to a massless scalar on flat space background to derive a result which is independent of the gauge parameters α and β [49]. The same technique has just been applied to quantum gravitational corrections to electrodynamics on flat space background [51], and strenuous efforts are underway to generalize it to de Sitter background [52]. The two flat space exercises demonstrate that gauge independent results typically show the same space–time dependence as in a fixed gauge, but with different numerical coefficients.…”

How Inflationary Gravitons Affect the Force of Gravity

“…It remains to renormalize the local divergence in Expression (47). This turns out to always produce a finite local term proportional to ln(a).…”

“…The large logarithms we have found all derive from terms that carry factors of H 2 , and their gauge dependence is not known, although indications from gravity plus electromagnetism suggest that there is some [32]. A procedure was developed for removing this gauge dependence [46], which has been successfully applied on a flat space background to graviton loop corrections to the massless, minimally coupled scalar [46] and to electromagnetism [47]. The massless, minimally coupled scalar exchange potential was identified as the simplest venue for generalizing this technique to the de Sitter background [35], and it is hoped that a result will be available later this year.…”

How Inflationary Gravitons Affect the Force of Gravity

“…It is interesting to compare the effect of graviton contributions to the dependence is not known, although indications from gravity plus electromagnetism suggest that there is some [33]. A procedure has been developed for removing this gauge dependence [42], which has been successfully applied on flat space background to graviton loop corrections to the massless, minimally coupled scalar [42], and to electromagnetism [43]. The massless, minimally coupled scalar exchange potential ha been identified as the simplest venue for generalizing this technique to de Sitter background [36], and it is hoped that a result will be available later this year.…”

“…The massless, minimally coupled scalar exchange potential ha been identified as the simplest venue for generalizing this technique to de Sitter background [36], and it is hoped that a result will be available later this year. Based on flat space background experience [42,43], we expect that the elimination of gauge dependence will not eliminate large graviton logarithms but might change their numerical coefficients.…”