1110.2999 (Pouria Pedram)

A Higher Order GUP with Minimal Length Uncertainty and Maximal Momentum    [PDF]

Pouria Pedram

We present a higher order Generalized (Gravitational) Uncertainty Principle (GUP) in the form $[X,P]=i\hbar/(1-\beta P^2)$. This form of GUP 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. Here we present two equivalent and exact representations where one is formally self-adjoint and naturally perturbative. We show that the presence of the maximal momentum results in an upper bound on the energy spectrum of the free particle, particle in box, and harmonic oscillator. We then generalize this GUP to D dimensions that will be shown it is noncommutative and find the invariant density of states. This form of GUP modifies the 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.

View original: http://arxiv.org/abs/1110.2999