We present a formulation of the generalized uncertainty principle based on commutator $[{\stackrel{^}{x}}^{i},{\stackrel{^}{p}}_{j}]$ between position and momentum operators defined in covariant manner using normal coordinates. show how any such can acquire corrections if space is curved. The correction completely determined by extrinsic curvature surface ${p}^{2}=\text{constant}$ space, result...

The concept of minimum length, widely accepted as a low-energy effect quantum gravity, manifests itself in mechanics through generalized uncertainty principles. Curved momentum space, on the other hand, is at heart similar applications such doubly special relativity. We introduce duality between theories yielding principles and nontrivial space. In particular, we find canonically conjugate vari...

Recently Chung and Hassanabadi proposed a higher order general uncertainty principle (GUP?) that predicts minimal length as well possesses upper bound momentum limit. In this article, we have discussed an ideal gas system its thermal properties using deformed canonical algebra introduced by them. Moreover, examined blackbody radiation spectrum the cosmological constant in presence of GUP?. Afte...

The emergence of the generalized uncertainty principle and existence a non-zero minimal length are intertwined. On other hand, Heisenberg forms core EPR paradox. Subsequently, here, implications resorting to (or equally, length) instead on quantum non-locality investigated by focusing Franson experiment in which energy-time entanglement is backbone understanding explaining results. survey also ...