Application of Biot–Savart law and generalized uncertainty principle

2019 ◽  
Vol 16 (04) ◽  
pp. 1950065 ◽  
Author(s):  
B. Khosropour ◽  
S. K. Moayedi
Keyword(s):  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Recent Decade ◽  
Minimal Length ◽  
Length Scale ◽  
Magnetostatic Field ◽  
Circular Loop ◽  
Straight Wire ◽  
Limit Formula ◽  
Minimal Length Scale

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.

scholarly journals Nonsingular universe from generalized thermostatistics

2016 ◽  
Vol 25 (02) ◽  
pp. 1650028
Author(s):  
B. Vakili ◽  
M. A. Gorji
Keyword(s):  
Statistical Mechanics ◽  
Uncertainty Principle ◽  
Quantum Cosmology ◽  
Generalized Uncertainty Principle ◽  
Friedmann Equation ◽  
Minimal Length ◽  
Loop Quantum Cosmology ◽  
Length Scale ◽  
Minimal Length Scale ◽  
Early Radiation

We study the statistical mechanics of the early radiation dominated universe in the context of a generalized uncertainty principle (GUP) which supports the existence of a minimal length scale. Utilizing the resultant modified thermodynamical quantities, we obtain a deformed Friedmann equation which is very similar to that arising from loop quantum cosmology scenarios. The energy and entropy densities get maximum bounds about Planck temperature and a nonsingular universe then emerges in this setup.

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 Effect of GUP on the Kepler problem and a variable minimal length

2014 ◽  
Vol 92 (6) ◽  
pp. 484-487 ◽  
Author(s):  
Fatemeh Ahmadi ◽  
Jafar Khodagholizadeh
Keyword(s):  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Kepler Problem ◽  
Rotational Symmetry ◽  
Generalized Uncertainty Principle ◽  
Space Time ◽  
Minimal Length ◽  
De Sitter ◽  
Heisenberg Uncertainty Principle ◽  
Perihelion Shift

Various approaches to quantum gravity, such as string theory, predict a minimal measurable length and a modification of the Heisenberg uncertainty principle near the Plank scale, known as the generalized uncertainty principle (GUP). Here we study the effects of GUP, which preserves the rotational symmetry of the space–time, on the Kepler problem. By comparing the value of the perihelion shift of the planet Mercury in Schwarzschild – de Sitter space–time with the resultant value of GUP, we find a relation between the minimal measurable length and the cosmological constant of the space–time. Now, if the cosmological constant varies with time, we have a variable minimal length in the space–time. Finally, we investigate the effects of GUP on the stability of circular orbits.

scholarly journals Exotic fermionic fields and minimal length

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
J. M. Hoff da Silva ◽  
D. Beghetto ◽  
R. T. Cavalcanti ◽  
R. da Rocha
Keyword(s):  
Dirac Equation ◽  
Quantum Gravity ◽  
Dirac Operator ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Dynamical Equations ◽  
Spacetime Manifold ◽  
Fermionic Fields

Abstract We investigate the effective Dirac equation, corrected by merging two scenarios that are expected to emerge towards the quantum gravity scale. Namely, the existence of a minimal length, implemented by the generalized uncertainty principle, and exotic spinors, associated with any non-trivial topology equipping the spacetime manifold. We show that the free fermionic dynamical equations, within the context of a minimal length, just allow for trivial solutions, a feature that is not shared by dynamical equations for exotic spinors. In fact, in this coalescing setup, the exoticity is shown to prevent the Dirac operator to be injective, allowing the existence of non-trivial solutions.

scholarly journals Heisenberg Algebra in the Bargmann-Fock Space with Natural Cutoffs

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Maryam Roushan ◽  
Kourosh Nozari
Keyword(s):  
Uncertainty Principle ◽  
Fock Space ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Maximal Momentum

We construct a Heisenberg algebra in Bargmann-Fock space in the presence of natural cutoffs encoded as minimal length, minimal momentum, and maximal momentum through a generalized uncertainty principle.

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 MICROSCOPIC BLACK HOLE AND UNCERTAINTY PRINCIPLE WITH MINIMAL LENGTH AND MOMENTUM

2013 ◽  
Vol 28 (10) ◽  
pp. 1350029 ◽  
Author(s):  
M. M. STETSKO
Keyword(s):  
Phase Transition ◽  
Heat Capacity ◽  
Black Hole ◽  
Uncertainty Principle ◽  
Emission Rate ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Schwarzschild Black Hole ◽  
Evaporation Time ◽  
Thermodynamical Functions

We investigate a microscopic black hole in the case of modified generalized uncertainty principle with a minimal uncertainty in position as well as in momentum. We calculate thermodynamical functions of a Schwarzschild black hole such as temperature, entropy and heat capacity. It is shown that the incorporation of minimal uncertainty in momentum leads to minimal temperature of a black hole. Minimal temperature gives rise to appearance of a phase transition. Emission rate equation and black hole's evaporation time are also obtained.

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