scholarly journals Generalized Uncertainty Principle in Quantum Cosmology for the Maximally Symmetric Space

2019 ◽  
Vol 64 (2) ◽  
pp. 100 ◽  
Author(s):  
V. E. Kuzmichev ◽  
V. V. Kuzmichev
Keyword(s):  
Symmetric Space ◽  
Uncertainty Principle ◽  
Uncertainty Relation ◽  
Generalized Uncertainty Principle ◽  
Solvable Model ◽  
Spacelike Hypersurface ◽  
Gravitational Systems ◽  
Exactly Solvable ◽  
Generalized Time ◽  
Canonical Quantum

The new uncertainty relation is derived in the context of the canonical quantum theory with gravity in the case of the maximally symmetric space. This relation establishes a connection between fluctuations of the quantities, which determine the intrinsic and extrinsic curvatures of the spacelike hypersurface in spacetime and introduces the uncertainty principle for quantum gravitational systems. The generalized time-energy uncertainty relation taking gravity into account gravity is proposed. It is shown that known Unruh’s uncertainty relation follows, as a particular case, from the new uncertainty relation. As an example, the sizes of fluctuations of the scale factor and its conjugate momentum are calculated within an exactly solvable model. All known modifications of the uncertainty principle deduced previously from different approaches in the theory of gravity and the string theory are obtained as particular cases of the proposed general expression.

scholarly journals Mathematical Uncertainty Relations and their Generalization for Multiple Incompatible Observables

2017 ◽  
Vol 33 (1) ◽  
Author(s):  
Hung Quang Nguyen ◽  
Tu Quang Bui
Keyword(s):  
Uncertainty Principle ◽  
Uncertainty Relation ◽  
Generalized Uncertainty Principle ◽  
Schwarz Inequality ◽  
Uncertainty Relations ◽  
Heisenberg Uncertainty Relation ◽  
Generalized Uncertainty Relation ◽  
Heisenberg Uncertainty ◽  
Incompatible Observables

We show that the famous Heisenberg uncertainty relation for two incompatible observables can be generalized elegantly to the determinant form for N arbitrary observables. To achieve this purpose, we propose a generalization of the Cauchy-Schwarz inequality for two sets of vectors. Simple consequences of the N-ary uncertainty relation are also discussed. Keywords: Generalized uncertainty relation, Generalized uncertainty principle, Generalized Cauchy-Schwarz inequality.

scholarly journals Entropic uncertainty relation based on generalized uncertainty principle

2017 ◽  
Vol 32 (28) ◽  
pp. 1750145 ◽  
Author(s):  
Li-Yi Hsu ◽  
Shoichi Kawamoto ◽  
Wen-Yu Wen
Keyword(s):  
Uncertainty Principle ◽  
Uncertainty Relation ◽  
Black Hole Physics ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Thought Experiments ◽  
Small Deformation ◽  
Entropic Uncertainty Relation ◽  
Deformation Parameters ◽  
Gaussian Wave Function

We explore the modification of the entropic formulation of uncertainty principle in quantum mechanics which measures the incompatibility of measurements in terms of Shannon entropy. The deformation in question is the type so-called generalized uncertainty principle that is motivated by thought experiments in quantum gravity and string theory and is characterized by a parameter of Planck scale. The corrections are evaluated for small deformation parameters by use of the Gaussian wave function and numerical calculation. As the generalized uncertainty principle has proven to be useful in the study of the quantum nature of black holes, this study would be a step toward introducing an information theory viewpoint to black hole physics.

scholarly journals Tsallis statistics and generalized uncertainty principle

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Giuseppe Gaetano Luciano
Keyword(s):  
Uncertainty Principle ◽  
Uncertainty Relation ◽  
Generalized Uncertainty Principle ◽  
Planck Scale ◽  
Unruh Effect ◽  
Heisenberg Uncertainty ◽  
Gaussian Statistics ◽  
Non Gaussian ◽  
Effective Description ◽  
Monotonic Relation

AbstractIt has been argued that non-Gaussian statistics provide a natural framework to investigate semiclassical effects in the context of Planck-scale deformations of the Heisenberg uncertainty relation. Here we substantiate this point by considering the Unruh effect as a specific playground. By working in the realm of quantum field theory, we reformulate the derivation of the modified Unruh effect from the generalized uncertainty principle (GUP) in the language of the nonextensive Tsallis thermostatistics. We find a nontrivial monotonic relation between the nonextensivity index q and the GUP deformation parameter $$\beta $$ β , which generalizes an earlier result obtained in quantum mechanics. We then extend our analysis to black hole thermodynamics. We preliminarily discuss our outcome in the broader context of an effective description of Planck-scale gravitational physics based on Tsallis theory.

The reduced α-amplitude in an exactly solvable model

1979 ◽  
Vol 324 (1) ◽  
pp. 173-181 ◽  
Author(s):  
T. Fliessbach ◽  
P. Manakos
Keyword(s):  
Solvable Model ◽  
Exactly Solvable Model ◽  
Exactly Solvable
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