Minimal length uncertainty relation and ultraviolet regularization

Kempf, Achim; Mangano, G.

doi:10.1103/physrevd.55.7909

Cited by 422 publications

(495 citation statements)

References 18 publications

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“…Let us focus attention on the study of the quantum cosmology of the model described by the Hamiltonian (8). The corresponding commutation relations are as follows…”

Section: The Modelmentioning

confidence: 99%

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Generalized uncertainty principle in Bianchi type I quantum cosmology

Vakili

Sepangi

2007

Physics Letters B

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We study a quantum Bianchi type I model in which the dynamical variables of the corresponding minisuperspace obey the generalized Heisenberg algebra. Such a generalized uncertainty principle has its origin in the existence of a minimal length suggested by quantum gravity and sting theory. We present approximate analytical solutions to the corresponding Wheeler-DeWitt equation in the limit where the scale factor of the universe is small and compare the results with the standard commutative and noncommutative quantum cosmology. Similarities and differences of these solutions are also discussed.

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“…Let us focus attention on the study of the quantum cosmology of the model described by the Hamiltonian (8). The corresponding commutation relations are as follows…”

Section: The Modelmentioning

confidence: 99%

“…An important feature of the existence of a minimal length is the modification of the standard Heisenberg commutation relation in the usual quantum mechanics [7,8]. Such relations are known as the Generalized Uncertainty Principle (GUP).…”

Section: Introductionmentioning

confidence: 99%

Generalized uncertainty principle in Bianchi type I quantum cosmology

Vakili

Sepangi

2007

Physics Letters B

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“…The problems with deformed Heisenberg algebra with small additions to the canonical commutational relations have been under a thorough and versatile scrutiny for a period of time [1][2][3][4][5][6][7][8][9][10]. Deformed commutational relations were studied for the first time in [11] where this issue was raised in connection with the idea of quantisation of space.…”

Section: Introductionmentioning

confidence: 99%

On Dirac theory in the space with deformed Heisenberg algebra: exact solutions

Vakarchuk¹

2005

J. Phys. A: Math. Gen.

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The Dirac equation has been studied in which the Dirac matricesα,β have space factors, respectively f and f 1 , dependent on the particle's space coordinates. The f function deforms Heisenberg algebra for the coordinates and momenta operators, the function f 1 being treated as a dependence of the particle mass on its position. The properties of these functions in the transition to the Schrödinger equation are discussed. The exact solution of the Dirac equation for the particle motion in the Coulomnb field with a linear dependence of the f function on the distance r to the force centre and the inverse dependence on r for the f 1 function has been found.

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“…It is an old idea [33,34] that a noncommutative modification of the algebraic structure of space-time could provide a regularization of the divergences of quantum field theory, because the representations of noncommutative 'spaces' have a lattice-like structure [25,22,26,20,5] which should automatically impose an ultraviolet cut-off [14,9]. This idea has been challenged recently from various points of view [21,8,28,29,32].…”

Section: Introductionmentioning

confidence: 99%

Geometrical Tools for Quantum Euclidean Spaces

Cerchiai

Fiore

Madore

2001

Commun. Math. Phys.

106

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We apply one of the formalisms of noncommutative geometry to R N q , the quantum space covariant under the quantum group SO q (N ). Over R N q there are two SO q (N )-covariant differential calculi. For each we find a frame, a metric and two torsion-free covariant derivatives which are metric compatible up to a conformal factor and which have a vanishing linear curvature. This generalizes results found in a previous article for the case of R 3 q . As in the case N = 3, one has to slightly enlarge the algebra R N q ; for N odd one needs only one new generator whereas for N even one needs two. As in the particular case N = 3 there is a conformal ambiguity in the natural metrics on the differential calculi over R N q . While in our previous article the frame was found 'by hand', here we disclose the crucial role of the quantum group covariance and exploit it in the construction. As an intermediate step, we find a homomorphism from the cross product of R N q with U q so(N ) into R N q , an interesting result in itself.

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Minimal length uncertainty relation and ultraviolet regularization

Cited by 422 publications

References 18 publications

Generalized uncertainty principle in Bianchi type I quantum cosmology

Generalized uncertainty principle in Bianchi type I quantum cosmology

On Dirac theory in the space with deformed Heisenberg algebra: exact solutions

Geometrical Tools for Quantum Euclidean Spaces

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