scholarly journals Modified Commutators vs Modified Operators in a Quantum Gravity minimal length scale

2021 ◽  
Author(s):  
Joey Contreras ◽  
Douglas Singleton ◽  
Michael Bishop ◽  
Jaeyeong Lee
Keyword(s):  
Quantum Gravity ◽  
Minimal Length ◽  
Length Scale ◽  
Minimal Length Scale

scholarly journals Modified commutators are not sufficient to determine a quantum gravity minimal length scale

2020 ◽  
Vol 802 ◽  
pp. 135209 ◽  
Author(s):  
Michael Bishop ◽  
Jaeyeong Lee ◽  
Douglas Singleton
Keyword(s):  
Quantum Gravity ◽  
Minimal Length ◽  
Length Scale ◽  
Minimal Length Scale

scholarly journals LAGRANGIAN FORMULATION OF A MAGNETOSTATIC FIELD IN THE PRESENCE OF A MINIMAL LENGTH SCALE BASED ON THE KEMPF ALGEBRA

2013 ◽  
Vol 28 (30) ◽  
pp. 1350142 ◽  
Author(s):  
S. K. MOAYEDI ◽  
M. R. SETARE ◽  
B. KHOSROPOUR
Keyword(s):  
Integral Form ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Lagrangian Formulation ◽  
Length Scale ◽  
Magnetostatic Field ◽  
Classical Level ◽  
Spatial Dimensions ◽  
Minimal Length Scale ◽  
The Relationship

In the 1990s, Kempf and his collaborators Mangano and Mann introduced a D-dimensional (β, β′)-two-parameter deformed Heisenberg algebra which leads to an isotropic minimal length [Formula: see text]. In this work, the Lagrangian formulation of a magnetostatic field in three spatial dimensions (D = 3) described by Kempf algebra is presented in the special case of β′ = 2β up to the first-order over β. We show that at the classical level there is a similarity between magnetostatics in the presence of a minimal length scale (modified magnetostatics) and the magnetostatic sector of the Abelian Lee–Wick model in three spatial dimensions. The integral form of Ampere's law and the energy density of a magnetostatic field in the modified magnetostatics are obtained. Also, the Biot–Savart law in the modified magnetostatics is found. By studying the effect of minimal length corrections to the gyromagnetic moment of the muon, we conclude that the upper bound on the isotropic minimal length scale in three spatial dimensions is 4.42×10-19m. The relationship between magnetostatics with a minimal length and the Gaete–Spallucci nonlocal magnetostatics [J. Phys. A: Math. Theor. 45, 065401 (2012)] is investigated.

scholarly journals Probing the minimal length scale by precision tests of the muon g−2

2004 ◽  
Vol 584 (1-2) ◽  
pp. 109-113 ◽  
Author(s):  
U. Harbach ◽  
S. Hossenfelder ◽  
M. Bleicher ◽  
H. Stöcker
Keyword(s):  
Minimal Length ◽  
Length Scale ◽  
Minimal Length Scale

scholarly journals Mass, Spacetime Symmetry, de Sitter Vacuum, and the Higgs Mechanism

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 634 ◽  
Author(s):  
Irina Dymnikova
Keyword(s):  
Higgs Mechanism ◽  
Minimal Length ◽  
Length Scale ◽  
False Vacuum ◽  
De Sitter ◽  
Negative Mass ◽  
Spacetime Symmetry ◽  
Generic Relation ◽  
Minimal Length Scale ◽  
De Sitter Vacuum

We address the question of the intrinsic relation between mass, gravity, spacetime symmetry, and the Higgs mechanism implied by involvement of the de Sitter vacuum as its basic ingredient (a false vacuum). Incorporating the de Sitter vacuum, the Higgs mechanism implicitly incorporates the generic relation between mass, gravity, and spacetime symmetry revealed in the frame of General Relativity for all objects involving the de Sitter vacuum. We overview two observational cases which display and verify this relation, the case known as “negative mass square problem” for neutrino, and appearance of a minimal length scale in e + e − annihilation.

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