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.