The Experts below are selected from a list of 8448 Experts worldwide ranked by ideXlab platform
Michele Maggiore - One of the best experts on this subject based on the ideXlab platform.
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quantum groups gravity and the generalized uncertainty principle
Physical Review D, 1994Co-Authors: Michele MaggioreAbstract:We investigate the relationship between the generalized uncertainty principle in quantum gravity and the quantum deformation of the Poincar\'e Algebra. We find that a deformed Newton-Wigner position operator and the generators of spatial translations and rotations of the deformed Poincar\'e Algebra obey a deformed Heisenberg Algebra from which the generalized uncertainty principle follows. The result indicates that in the $\ensuremath{\kappa}$-deformed Poincar\'e Algebra a minimal observable length emerges naturally.
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the Algebraic structure of the generalized uncertainty principle
Physics Letters B, 1993Co-Authors: Michele MaggioreAbstract:We show 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. The deformed Algebra and therefore the form of the generalized uncertainty principle are fixed uniquely by rather simple assumptions. The string theory result is reproduced expanding our result at first order in Δp/MPL. We also briefly comment on possible implications for Lorentz at the Planck scale.
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the Algebraic structure of the generalized uncertainty principle
arXiv: High Energy Physics - Theory, 1993Co-Authors: Michele MaggioreAbstract:We show that a deformation of the Heisenberg Algebra which depends on a dimensionful parameter $\kappa$ is the Algebraic structure which underlies the generalized uncertainty principle in quantum gravity. The deformed Algebra and therefore the form of the generalized uncertainty principle are fixed uniquely by rather simple assumptions. The string theory result is reproduced expanding our result at first order in $\Delta p/M_{\rm PL}$. We also briefly comment on possible implications for Lorentz invariance at the Planck scale.
V M Tkachuk - One of the best experts on this subject based on the ideXlab platform.
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deformed Heisenberg Algebra with minimal length and the equivalence principle
Physical Review A, 2012Co-Authors: V M TkachukAbstract:Studies in string theory and quantum gravity lead to the Generalized Uncertainty Principle (GUP) and suggest the existence of a fundamental minimal length which, as was established, can be obtained within the deformed Heisenberg Algebra. The first look on the classical motion of bodies in a space with corresponding deformed Poisson brackets in a uniform gravitational field can give an impression that bodies of different mass fall in different ways and thus the equivalence principle is violated. Analyzing the kinetic energy of a composite body we find that the motion of its center of mass in the deformed space depends on some effective parameter of deformation. It gives a possibility to recover the equivalence principle in the space with deformed Poisson brackets. and thus GUP is reconciled with the equivalence principle. We also show that the independence of kinetic energy on composition leads to the recovering of the equivalence principle in the space with deformed Poisson brackets.
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scattering problem in deformed space with minimal length
Physical Review A, 2007Co-Authors: M M Stetsko, V M TkachukAbstract:We investigated the elastic scattering problem with deformed Heisenberg Algebra leading to the existence of a minimal length. The continuity equations for the moving particle in deformed space were constructed. We obtained the Green's function for a free particle, the scattering amplitude, and the cross section in deformed space. We also calculated the scattering amplitudes and differential cross sections for the Yukawa and the Coulomb potentials in the Born approximation.
Mushtaq B Shah - One of the best experts on this subject based on the ideXlab platform.
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the most general form of deformation of the Heisenberg Algebra from the generalized uncertainty principle
Physics Letters B, 2016Co-Authors: Syed Athar Masood, Mir Faizal, Jamil Raza, Mushtaq B ShahAbstract:Abstract In this paper, we will propose the most general form of the deformation of Heisenberg Algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg Algebra will deform all quantum mechanical systems. The form of the generalized uncertainty principle used to motivate these results will be motivated by the space fractional quantum mechanics, and non-locality in quantum mechanical systems. We also analyse a specific limit of this generalized deformation for one dimensional system, and in that limit, a nonlocal deformation of the momentum operator generates a local deformation of all one dimensional quantum mechanical systems. We analyse the low energy effects of this deformation on a harmonic oscillator, Landau levels, Lamb shift, and potential barrier. We also demonstrate that this deformation leads to a discretization of space.
Mir Faizal - One of the best experts on this subject based on the ideXlab platform.
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the most general form of deformation of the Heisenberg Algebra from the generalized uncertainty principle
Physics Letters B, 2016Co-Authors: Syed Athar Masood, Mir Faizal, Jamil Raza, Mushtaq B ShahAbstract:Abstract In this paper, we will propose the most general form of the deformation of Heisenberg Algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg Algebra will deform all quantum mechanical systems. The form of the generalized uncertainty principle used to motivate these results will be motivated by the space fractional quantum mechanics, and non-locality in quantum mechanical systems. We also analyse a specific limit of this generalized deformation for one dimensional system, and in that limit, a nonlocal deformation of the momentum operator generates a local deformation of all one dimensional quantum mechanical systems. We analyse the low energy effects of this deformation on a harmonic oscillator, Landau levels, Lamb shift, and potential barrier. We also demonstrate that this deformation leads to a discretization of space.
Carlos Castro - One of the best experts on this subject based on the ideXlab platform.
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extended lorentz transformations in clifford space relativity theory
viXra, 2014Co-Authors: Carlos CastroAbstract:Some novel physical consequences of the Extended Relativity Theory in $C$-spaces (Clifford spaces) were explored recently. In particular, generalized photon dispersion relations allowed for energy-dependent speeds of propagation while still $retaining$ the Lorentz symmetry in ordinary spacetimes, but breaking the $extended$ Lorentz symmetry in $C$-spaces. In this work we analyze in further detail the extended Lorentz transformations in Clifford Space and their physical implications. Based on the notion of ``extended events" one finds a very different physical explanation of the phenomenon of ``relativity of locality" than the one described by the Doubly Special Relativity (DSR) framework. A generalized Weyl-Heisenberg Algebra, involving polyvector-valued coordinates and momenta operators, furnishes a realization of an extended Poincare Algebra in $C$-spaces. In addition to the Planck constant $\hbar$, one finds that the commutator of the Clifford scalar components of the Weyl-Heisenberg Algebra requires the introduction of a $dimensionless$ parameter which is expressed in terms of the ratio of two length scales : the Planck and Hubble scales. We finalize by discussing the concept of ``photons", null intervals, effective temporal variables and the addition/subtraction laws of generalized velocities in $C$-space.
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on modified weyl Heisenberg Algebras noncommutativity matrix valued planck constant and qm in clifford spaces
viXra, 2009Co-Authors: Carlos CastroAbstract:A novel Weyl-Heisenberg Algebra in Clifford-spaces is constructed that is based on a matrix-valued HAB extension of Planck's constant. As a result of this modifiedWeyl-Heisenberg Algebra one will no longer be able to measure, simultaneously, the pairs of variables (x, px); (x, py); (x, pz); (y, px), ... with absolute precision. New Klein-Gordon and Dirac wave equations and dispersion relations in Clifford-spaces are presented. The latter Dirac equation is a generalization of the Dirac-Lanczos-Barut-Hestenes equation. We display the explicit isomorphism between Yang's Noncommutative space-time Algebra and the area-coordinates Algebra associated with Clifford spaces. The former Yang's Algebra involves noncommuting coordinates and momenta with a minimum Planck scale λ (ultraviolet cutoff) and a minimum momentum p = ℏ/R (maximal length R, infrared cutoff ). The double-scaling limit of Yang's Algebra λ → 0, R → ∞, in conjunction with the large n → ∞ limit, leads naturally to the area quantization condition λR = L2 = nλ2 ( in Planck area units ) given in terms of the discrete angular-momentum eigenvalues n. It is shown how Modified Newtonian dynamics is also a consequence of Yang's Algebra resulting from the modified Poisson brackets. Finally, another noncommutative Algebra ( which differs from the Yang's Algebra ) and related to the minimal length uncertainty relations is presented . We conclude with a discussion of the implications of Noncommutative QM and QFT's in Clifford-spaces.
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on modified weyl Heisenberg Algebras noncommutativity matrix valued planck constant and qm in clifford spaces
Journal of Physics A, 2006Co-Authors: Carlos CastroAbstract:A novel Weyl–Heisenberg Algebra in Clifford spaces is constructed that is based on a matrix-valued extension of Planck's constant. As a result of this modified Weyl–Heisenberg Algebra one will no longer be able to measure, simultaneously, the pairs of variables (x, px), (x, py), (x, pz), (y, px), ... with absolute precision. New Klein–Gordon and Dirac wave equations and dispersion relations in Clifford spaces are presented. The latter Dirac equation is a generalization of the Dirac–Lanczos–Barut–Hestenes equation. We display the explicit isomorphism between Yang's noncommutative spacetime Algebra and the area-coordinates Algebra associated with Clifford spaces. The former Yang's Algebra involves noncommuting coordinates and momenta with a minimum Planck scale λ (ultraviolet cutoff) and a minimum momentum p = /R (maximal length R, infrared cutoff). The double-scaling limit of Yang's Algebra λ → 0, R → ∞, in conjunction with the large n → ∞ limit, leads naturally to the area quantization condition λR = L2 = nλ2 (in Planck area units) given in terms of the discrete angular-momentum eigenvalues n. It is shown how modified Newtonian dynamics is also a consequence of Yang's Algebra resulting from the modified Poisson brackets. Finally, another noncommutative Algebra which differs from Yang's Algebra and related to the minimal length uncertainty relations is presented. We conclude with a discussion of the implications of noncommutative QM and QFT's in Clifford spaces.