Related papers: Generalised uncertainty relations for angular mome…
Various theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Principle near the Planck scale to a so-called Generalized Uncertainty Principle (GUP). In some recent papers, we showed that the GUP gives rise to…
We present the coherent states of the harmonic oscillator in the framework of the generalized (gravitational) uncertainty principle (GUP). This form of GUP is consistent with various theories of quantum gravity such as string theory, loop…
We present a formulation of the generalised uncertainty principle based on commutator $\left[ {\hat x}^i, {\hat p}_j \right]$ between position and momentum operators defined in a covariant manner using normal coordinates. We show how any…
A general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed. We derive conditions which determine whether a given smooth function of the particle's variances and its covariance is…
The non-relativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined in $D$-dimensional free particle and harmonic oscillator systems. The Feynman propagators for these systems are exactly derived within the…
Various theories of quantum gravity predict the existence of a minimum length scale, which leads to the modification of the standard uncertainty principle to the Generalized Uncertainty Principle (GUP). In this paper, we study two forms of…
We study coherent states associated to a generalized uncertainty principle (GUP). We separately analyze the cases of positive and negative deformation parameter $\beta$, showing that the ensuing probability distribution is a Tsallis…
We review highlights from string theory, black hole physics and doubly special relativity and some "thought" experiments which were suggested to probe the shortest distance and/or the maximum momentum at the Planck scale. The models which…
When minimal length uncertainty emerging from generalized uncertainty principle (GUP) is thoughtfully implemented, it is of great interest to consider its impacts on {\it "gravitational} Einstein field equations (gEFE) and to try to find…
We investigate the relationship between the generalized uncertainty principle in quantum gravity and the quantum deformation of the Poincar\'e algebra. We find that a deformed Newton-Wigner position operator and the generators of spatial…
In this work, we consider generalized uncertainty principles (GUPs) that incorporate a minimal length through generic momentum-dependent deformation functions. We thus develop a systematic approach connecting such a framework to effective…
Based on string theory, black hole physics, doubly special relativity and some "thought" experiments, minimal distance and/or maximum momentum are proposed. As alternatives to the generalized uncertainty principle (GUP), the modified…
The Generalized Uncertainty Principle (GUP) is a modification of Heisenberg's Principle predicted by several theories of Quantum Gravity. It consists of a modified commutator between position and momentum. In this work we compute…
We derive new space-time uncertainty relations (STUR) at the fundamental Planck length $L_P$ from quantum mechanics and general relativity (GR), both in flat and curved backgrounds. Contrary to claims present in the literature, our approach…
The effects of noncommutativity and of the existence of a minimal length on the phase space of a dilatonic cosmological model are investigated. The existence of a minimum length, results in the Generalized Uncertainty Principle (GUP), which…
There are several theoretical indications that the quantum gravity approaches may have predictions for a minimal measurable length, and a maximal observable momentum and throughout a generalization for Heisenberg uncertainty principle. The…
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…
We show that the existence of a minimum measurable length and the related Generalized Uncertainty Principle (GUP), predicted by theories of Quantum Gravity, influence all quantum Hamiltonians. Thus, they predict quantum gravity corrections…
Modifications in quantum mechanical phase space lead to the changes in the Heisenberg uncertainty principle, which can result in the Generalized Uncertainty Principle (GUP) or the Extended Uncertainty Principle (EUP), introducing quantum…
In this work, we point out an overlooked and subtle feature of the generalized uncertainty principle (GUP) approach to quantizing gravity: namely that different pairs of modified operators with the same modified commutator,…