One-loop corrections to the photon propagator in curved-space QED

We calculate and discuss the one-loop corrections to the photon sector of QED interacting to a background gravitational field. At high energies the fermion field can be taken as massless and the quantum terms can be obtained by integrating conformal anomaly. We present a covariant local expression for the corresponding effective action, similar to the one obtained earlier for the gravitational sector. At the moderate energies the quantum terms can be obtained through the heat-kernel method. In this way we derive the exact one-loop $\beta$ function for the electric charge in the momentum subtraction scheme and explore both massless and large-mass limits. The relation between the two approaches is shown and the difference discussed in view of the possible applications to cosmology and astrophysics.

Figure 1

The beta functions corresponding to form factors $k_1$ (solid line) and $k_2$ (dashed line). The vertical axis is drawn in units of $e^3/(4\pi {)}^2$.

Figure 2

The curves for the running parameter $e(t{)}^2$ seem to coincide for both MS and physical scheme (in the last one we use the prescription corresponding to the form factor $k_1$). Actually, both curves are slightly different as well as the Landau pole (see Fig. 3). We have used $e(0)=0.1$.

Figure 3

The same plot as in Fig. 2, viewed with more detail around $t\sim 5900$. Here the two vertical lines indicate different Landau poles. The dashed line corresponds to the MS scheme. The value for $t$ corresponding to the poles differs from each other by less than 0.02%.

Figure 4

Curves for $e(t{)}^{-2}$. The dashed line corresponds to the MS scheme and the solid line for the momentum subtraction scheme. For higher $t$, both curves are parallel straight lines. Substantial difference between the two plots takes place for $t<1$.