Symmetrized operators or modified integration measure in Generalized Uncertainty Principle Models

One feature of many Generalized Uncertainty Principle (GUP) models is that one needs to modify the measure of integration of the inner product in order for the modified operators (e.g.

the position or momentum operator) to be symmetric. In this short talk, I show that this same result can be achieved by symmetrizing the modified operators rather than changing the inner product of states. This leaves the momentum space unmodified, allowing for the eigenstates and maximally localized states of the modified position operator to have both momentum and standard position representations. This resolves the difficulties of GUP models having no standard position representation. I then discuss the difference in the two approaches and highlight the relative merits of each scheme.