Hilbert space representation of the minimal length uncertainty relation.
TL;DR: The quantum mechanical structure which underlies the generalized uncertainty relation which quantum theoretically describes the minimal length as a minimal uncertainty in position measurements is studied.
read more
Abstract: The existence of a minimal observable length has long been suggested in quantum gravity as well as in string theory. In this context a generalized uncertainty relation has been derived which quantum theoretically describes the minimal length as a minimal uncertainty in position measurements. Here we study in full detail the quantum mechanical structure which underlies this uncertainty relation. DAMTP/94-105, hep-th/9412167, and Phys.Rev.D52:1108 (1995)
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
30 years in: Quo vadis generalized uncertainty principle?
Pasquale Bosso,Giuseppe Gaetano Luciano,Luciano Petruzziello,Fabian Wagner +3 more
TL;DR: The generalized uncertainty principle is a modified version of Heisenberg's uncertainty principle that applies to the Planck scale. It has been subject to recent criticisms due to its conceptual shortcomings and lack of rigor.
38
Noncommutative Differential Forms on the kappa-deformed Space
TL;DR: In this article, a differential algebra of forms on the kappa-deformed space was constructed and the exterior derivative of one-forms was shown to satisfy the graded Jacobi identity.
38
Dirac oscillator and nonrelativistic Snyder-de Sitter algebra
TL;DR: In this article, a three dimensional Dirac oscillator was considered in space with deformed commutation relations known as Snyder-de Sitter algebra, which give rise to appearance of minimal uncertainties in position as well as in momentum.
38
Modified Unequal Mixture Scalar Vector Hulthén–Yukawa Potentials Model as a Quark–Antiquark Interaction and Neutral Atoms via Relativistic Treatment Using the Improved Approximation of the Centrifugal Term and Bopp’s Shift Method
TL;DR: In this paper, a modified Klein-Gordon containing an interaction of the modified unequal mixture scalar vector Hulthen-Yukawa potentials model (MUMSVHYa-PM) using the procedure of improved approximation of the centrifugal term, Bopp's shift method and perturbation theory is presented.
37
Towards a cosmology with minimal length and maximal energy
Ahmed Farag Ali,Barun Majumder +1 more
TL;DR: In this paper, the Friedmann-Robertson-Walker (FRW) universe and Bianchi I, II universes are investigated in the framework of the generalized uncertainty principle (GUP) with a linear and a quadratic term in Planck length and momentum, which predicts the minimum measurable length as well as maximum measurable momentum.
37
References
Can spacetime be probed below the string size
TL;DR: In this paper, it was shown that if the energy is not so extreme to cause a gravitational instability and when the scattering angle approaches some critical value from below, the distance starts increasing, thus departing from the usual position-momentum uncertainty relation, and in no instance is the resolution smaller than the string length.
1.7K
Spacetime quantization induced by classical gravity
TL;DR: In this article, the authors propose spacetime uncertainty relations motivated by Heisenberg's uncertainty principle and by Einstein's theory of classical gravity, which is described by a non-commutative algebra whose commutation relations do imply our uncertainty relations.
1K
Minimum physical length and the generalized uncertainty principle in string theory
TL;DR: In this article, a possible definition of path integrals for string theory is studied, based on a discretized version of Polyakov's generating functional, and the finite resolution of string theory, as opposed to the infinite resolution in particle theory, clearly emerges from a renormalization group type analysis.
903
The algebraic structure of the generalized uncertainty principle
TL;DR: In this article, it was shown that a deformation of the Heisenberg algebra which depends on a dimensionful parameter κ is the algebraic structure which underlies the generalized uncertainty principle in quantum gravity.
741