We study sharp second order inequalities of Caffarelli-Kohn-Nirenberg type in the euclidian space R N , where denotes dimension. This analysis is equivalent to uncertainty principles for special classes vector fields. In particular, we show that when switching from scalar fields u : n ? C form = ? U ( being a field) best constant Heisenberg Uncertainty Principle (HUP) increases 2 4 + ) and opti...