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String theory, quantum geometry, loop quantum gravity and black hole physics all indicate the existence of a minimal observable length on the order of Planck length. This feature leads to a modification of Heisenberg uncertainty principle.…

Different candidates of Quantum Gravity such as String Theory, Doubly Special Relativity, Loop Quantum Gravity and black hole physics all predict the existence of a minimum observable length or a maximum observable momentum which modifies…

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 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…

The prediction of a minimal length scale by various quantum gravity candidates (such as string/M theory, Doubly Special Relativity, Loop Quantum Gravity and others) have suggested modification of Heisenberg Uncertainty Principle (HUP),…

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…

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,…

Existence of a minimal measurable length and an upper bound for the momentum fluctuations are the casting reasons for generalization of uncertainty principle and then reformulation of Hilbert space representation of quantum mechanics. In…

We extend significantly previous works on the Hilbert space representations of the Generalized Uncertainty Principle (GUP) in 3+1 dimensions of the form $[X_i,P_j] = i F_{ij}$ where $ F_{ij} = f(P^2) \delta_{ij} + g(P^2) P_i P_j $ for any…

One can use the generalized uncertainty principle (GUP) to incorporate the minimum measurable length in quantum gravity. It may be interesting to have a minimal time interval as well as the minimal length in the relativistic version of…

Many theories that attempt to formulate a quantum description of gravity suggest the existence of a fundamental minimum length scale. A popular method for incorporating this minimum length is through a modification of the Heisenberg…

The existence of a minimum observable length and/or a maximum observable momentum is in agreement with various candidates of quantum gravity such as string theory, loop quantum gravity, doubly special relativity and black hole physics. In…

This paper proposes a new high-order generalized uncertainty principle, which can modify the momentum operator and position operator simultaneously. Moreover, the new form of GUP is consistent with the viewpoint of the existence of the…

We investigate an extension of the Generalized Uncertainty Principle (GUP) in three dimensions by modifying the three dimensional position and momentum operators in a manner that remains coordinate-independent and retains as much of the…

We propose the generalized uncertainty principle (GUP) with an additional term of quadratic momentum motivated by string theory and black hole physics as a quantum mechanical framework for the minimal length uncertainty at the Planck scale.…

Various approaches to Quantum Gravity (such as String Theory and Doubly Special Relativity), as well as black hole physics predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg…

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…

Attempts to formulate a quantum theory of gravitation are collectively known as {\it quantum gravity}. Various approaches to quantum gravity such as string theory and loop quantum gravity, as well as black hole physics and doubly special…

Based on quantum mechanical framework for the minimal length uncertainty, we demonstrate that the generalized uncertainty principle (GUP) parameter could be best constrained by recent gravitational waves observations on one hand. On other…

Existence of minimal length is suggested in any quantum theory of gravity such as string theory, double special relativity and black hole physics. One way to impose minimal length is deforming Heisenberg algebra in phase space which is…