• one-loop renormalization
• Lorentz violations
• general relativity
• general linear electrodynamics
• birefringence
• Bhabha scattering
• Batalin-Vilkovisky
• anomalous magnetic moment
• QED
• ray-optically invisible non-metric deviations

The most general theory of electrodynamics with linear field equations contains an eleven-parameter family of geometries that deviate from a metric background and are effectively invisible to ray optics. The goal of this thesis is to show that these ray-optically invisible non-metric deviations produce detectable effects in quantum scatterings. As a consequence, quantum experiments provide a useful tool to detect and measure the effects of a non-metric geometry.
To show this, we first develop the pertinent quantum electrodynamics and discuss its renormalization. In particular, we quantize the theory à la Batalin-Vilkovisky and prove that it is renormalizable at every loop order in a gauge-invariant way. This way, electrodynamics with ray-optically invisible non-metricities provides a fundamental quantum theory of the electromagnetic interactions and can be used to investigate quantum effects at any loop order.
Concretely, we compute the effects of the non-metric deviations in the cross-sections of two prototypical scattering processes, namely e+ e- --> \bar{f} f and Bhabha scattering. In addition, we calculate the anomalous magnetic moment of the electron at the same loop order as it is known in standard QED. Notably, this last result allows us to find the precise value of one particular combination of the fine-structure constant and one of the eleven geometric degrees of freedom in which the considered geometries can deviate from a metric.
The dynamics of the non-metric deviations, on whose presence this thesis builds, has been determined recently. The gravitational field equations contain nine independent constants that need to be determined by experiments, compared to only two such constants---Newton's and the cosmological one---in general relativity. In the future, we expect to determine the values---or a least a bound---of these constants by combining the findings of this thesis with the gravitational theory.