Using Particle Physics Phenomena to Constrain Deviations from Quantum Mechanics

One way to better understand the foundations of quantum mechanics (QM) is to generalize its mathematical structure and examine the consequences of the resulting formalism. The primary aim of such an exercise is not to propose an empirical competitor to QM, but to clarify the structure of QM itself. The advantages of doing this study are twofold. Firstly, it can inform us of the robustness of the aspects that were generalized, and can be used as a precision test of QM. Secondly, these generalized theories could lead to phenomenology not present in canonical QM, and hence act as toy models for a more fundamental theory such as quantum gravity. We will present our work on a particular generalization of QM, in which the deviation from QM is quantified by means of two "deformation" parameters. We'll comment on how to use particle physics phenomena to constrain those parameters, as well as the possibility of witnessing phenomena beyond QM.