Curved Momentum-Space Equivalent to the Linear and Quadratic Generalized Uncertainty Principle

In this work, we deepen the correspondence between Generalized Uncertainty Principles and quantum dynamics on curved momentum space. In particular, we investigate the linear and quadratic Generalized Uncertainty Principle. Similar to earlier work, the resulting curvature tensor in the dual theory is proportional to the coordinate non-commutativity of the original formulation.