The prime example of quantum field theory (QFT) in background gauge fields is *quantum electrodynamics in external potentials*, which can be used to compute *vacuum polarization* (a contribution to the Lamb shift) or the *Schwinger effect*, the creation of electron/positron pairs in strong electric fields (one of the most important yet unconfirmed predictions of QFT). QFT in background gauge fields is also a practical calculational tool, via the *background field method*. Another instance is *perturbative quantum gravity*, where one quantizes the gravitational fluctuations around classical space-time geometries. We are interested in all these aspects of QFT in background gauge fields.

In QFT in in background gauge fields, one faces similar difficulties as for QFT on curved space-times (QFTCS). For generic background fields, translation invariance is broken, so that the powerful momentum space techniques can not be used. Also Wick rotation (analytic continuation) is not available. Furthermore, there is no preferred vacuum state in the presence of generic background gauge fields. For the study of QFT in background gauge fields, we thus proceed analogously to the modern treatment of QFTCS, i.e., using the mathematical tool of *microlocal analysis* and with an emphasis on *local (gauge) covariance* and the *local algebras of observables*.

Some topics studied in our group are:

Further reading regarding the topic of local gauge covariance: