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

We present a novel generalization of the Heisenberg uncertainty principle which introduces the existence of a maximal observable momentum and at the same time does not entail a minimal indeterminacy in position. The above result is an exact generalized uncertainty principle (GUP), valid at all energy scales. For small values of the deformation parameter beta, our ansatz is consistent with the usual expression for GUP borrowed from string theory, doubly special relativity and other quantum gravity candidates that provide beta with a negative sign. As a preliminary analysis, we study the implications of this new model on some quantum mechanical applications and on the black hole thermodynamics.