In trying to understand something about Quantum Field Theories and especially the mathematics behind them (or lack thereof) I have a hard time harvesting a handful of well defined examples (other than the free scalar field).
In the hope it will grant me a better understanding of what a QFT is or is not, I would kindly ask anyone knowing of some well defined examples, wheter toy models or something more involved, if they could point some references or even briefly sketch some constructions.