Symmetrized operators or modified integration measure in Generalized Uncertainty Principle Models

Abstract: Many Generalized Uncertainty Principle (GUP) models modify the inner-product measure to ensure symmetric position or momentum operators. We show that an alternate approach to these GUPs is to symmetrize the operators rather than modifying the inner product. This preserves the standard momentum space allowing the eigenstates and maximally localized states of the modified position operator to have a standard position representation. We compare both approaches and highlight their merits.