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

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.

2019 ◽  
Vol 16 (04) ◽  
pp. 1950065 ◽  
Author(s):  
B. Khosropour ◽  
S. K. Moayedi

In the recent decade, many investigations have been done in the framework of generalized uncertainty principle (GUP), but the phenomenology of models in this framework are less studied. In this work, the applications of Biot–Savart law in the presence of a minimal length scale are investigated. We obtain the modified magnetostatic field from an infinitely long, straight wire carrying current [Formula: see text]. Also, the modified magnetostatic field from a circular loop carrying current [Formula: see text] and the modified magnetostatic field of an ideal solenoid are found. It is interesting to note that in the limit [Formula: see text], all of the modified magnetostatic fields become their usual forms.


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

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 634 ◽  
Author(s):  
Irina Dymnikova

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.


2021 ◽  
Author(s):  
Joey Contreras ◽  
Douglas Singleton ◽  
Michael Bishop ◽  
Jaeyeong Lee

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