Formal developments in curved momentum space: the quantum field theory roadmap

We advocate that the dual picture of spacetime noncommutativity , i.e. the existence of a curved momentum space, could be a way out to solve some of the open conceptual problems in the field, such as the basis dependence of observables. In this framework, we show how to build deformed Klein--Gordon and Dirac equations. In addition, we give an outlook of how one could define quantum field theories, both free and interacting ones.