Related papers: Non-commutative space-time and the uncertainty pri…
Quantum gravity theories predict a minimal length at the order of magnitude of the Planck length, under which the concepts of space and time lose every physical meaning. In quantum mechanics, the insurgence of such minimal length can be…
We aim to analyze the consistency of the deformation of the Heisenberg algebra in the setting of constrained Hamiltonian systems, providing a procedure to induce the deformation on the Poisson algebra after symplectic reduction. We…
We show that the Euclidean Snyder non-commutative space implies infinitely many different physical predictions. The distinct frameworks are specified by generalized uncertainty relations underlying deformed Heisenberg algebras. Considering…
The Heisenberg uncertainty principle is known to be connected to the entropic uncertainty principle. This correspondence is obtained employing a Gaussian probability distribution for wave functions associated to the Shannon entropy.…
Studies in string theory and quantum gravity lead to the Generalized Uncertainty Principle (GUP) and suggest the existence of a fundamental minimal length which, as was established, can be obtained within the deformed Heisenberg algebra.…
Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of…
Generalized Uncertainty Principle (GUP) was obtained in string theory and quantum gravity and suggested the existence of a fundamental minimal length which, as was established, can be obtained within the deformed Heisenberg algebra. We use…
The Generalized Uncertainty Principle and the related minimum length are normally considered in non-relativistic Quantum Mechanics. Extending it to relativistic theories is important for having a Lorentz invariant minimum length and for…
Quantum gravity models predict a minimal measurable length which gives rise to a modification in the uncertainty principle. One of the simplest manifestations of these generalised uncertainty principles is the linear quadratic generalised…
Various deformations of the position-momentum algebras operators have been proposed. Their implications for single systems like the hydrogen atom or the harmonic oscillator have been addressed. In this paper we investigate the consequences…
Measurement outcomes of a quantum state can be genuinely random (unpredictable) according to the basic laws of quantum mechanics. The Heisenberg-Robertson uncertainty relation puts constrains on the accuracy of two noncommuting observables.…
Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of…
The Basic Universal Deformation Formula is proven and applied to show that Weyl algebras, which encode Heisenberg's uncertainty principle, are effective deformations of polynomial rings, and that uncertainty is necessary for stability.…
Starting from deformed quantum Heisenberg Lie algebras some realizations are given in terms of the usual creation and annihilation operators of the standard harmonic oscillator. Then the associated algebra eigenstates are computed and give…
In this paper, we clarify a foundational loose end affecting the phenomenological approach to quantum gravity centered around the generalization of Heisenberg uncertainty principle. This misconception stems from a series of recently…
It is generally argued that the combined effect of Heisenberg principle and general relativity leads to a minimum time uncertainty. Most of the analyses supporting this conclusion are based on a perturbative approach to quantization. We…
In this paper, the quantization and generalized uncertainty relation for some quantum deformed algebras are investigated. For several deformed algebras, the commutation relation between the position and the momentum operator is shown to be…
Various models of quantum gravity suggest a modification of the Heisenberg's Uncertainty Principle, to the so-called Generalized Uncertainty Principle, between position and momentum. In this work we show how this modification influences the…
Some fundamental aspects related with the construction of Robertson-Schr\"odinger like uncertainty principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum…
Heisenberg's uncertainty relation is commonly regarded as defining a level of unpredictability that is fundamentally incompatible with the deterministic laws embodied in classical field theories such as Einstein's general relativity. We…