How can I do quantum chemistry with QED?
From a theoretical chemists point of view, the inclusion of Quantum Electrodynamics (QED) can be very interesting if you are interested in radiaton-matter interactions, where the radiation field is quantized (commonly in the Coulomb gauge leading to a non-covariant quantization). This would include all types of absorption and emission processes but additionally also intermolecular dipole-dipole coupling, for example. If you are interested in this topic, I can highly recommend the textbook on Molecular Quantum Electrodynamics by Craig and Thirunamachandran.
Additionally, there is a very fascinating field studying atoms and molecules in cavities, i.e. in the framework of cavity-QED. In this context, a whole bunch of interesting new phenomena emerge, e.g. the Born-Oppenheimer-approximation needs to be reformulated, due to the full quantum description of the radiation field and the molecular degrees of freedom. You can consider https://arxiv.org/abs/1609.03901, if you are interested in getting an idea of this subject.