  In a recent paper, we presented a nonperturbative higher order generalized
uncertainty principle (GUP) that is consistent with various proposals of
quantum gravity such as string theory, loop quantum gravity, doubly special
relativity, and predicts both a minimal length uncertainty and a maximal
observable momentum. In this Letter, we find exact maximally localized states
and present a formally self-adjoint and naturally perturbative representation
of this modified algebra. Then we extend this GUP to D dimensions that will be
shown it is noncommutative and find invariant density of states. We show that
the presence of the maximal momentum results in upper bounds on the energy
spectrum of the free particle and the particle in box. Moreover, this form of
GUP modifies blackbody radiation spectrum at high frequencies and predicts a
finite cosmological constant. Although it does not solve the cosmological
constant problem, it gives a better estimation with respect to the presence of
just the minimal length.
