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We present a novel generalization of the Heisenberg uncertainty principlewhich introduces the existence of a maximal observable momentum and at the sametime does not entail a minimal indeterminacy in position. The above result isan exact generalized uncertainty principle (GUP), valid at all energy scales.For small values of the deformation parameter $\beta$, our ansatz is consistentwith the usual expression for GUP borrowed from string theory, doubly specialrelativity and other quantum gravity candidates that provide $\beta$ with anegative sign. As a preliminary analysis, we study the implications of this newmodel on some quantum mechanical applications and on the black holethermodynamics.

Generalized uncertainty principle with maximal observable momentum and no minimal length indeterminacy