Noncommutative Quantum Mechanics and Quantum Cosmology

Bastos, Catarina; Bertolami, Orfeu; Dias, Nuno Costa; Prata, João Nuno

doi:10.1142/s0217751x09046138

Cited by 30 publications

(19 citation statements)

References 18 publications

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“…In the context of string and M-theory, a configuration space noncommutativity arises as the low-energy effective theory of a D-brane in the background of a Neveu-Schwarz B field living in a space with spatial noncommutativity [1]. More recently, various aspects of noncommutative quantum field theory [4,5] and quantum mechanics [6][7][8][9][10] have been investigated.…”

Section: Introductionmentioning

confidence: 99%

Noncanonical phase-space noncommutativity and the Kantowski-Sachs singularity for black holes

Bastos¹,

Bertolami

Dias

et al. 2011

Phys. Rev. D

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We consider a cosmological model based upon a noncanonical noncommutative extension of the Heisenberg-Weyl algebra to address the thermodynamical stability and the singularity problem of black holes whose interior are described by the Kantowski-Sachs metric and modeled by a noncommutative extension of the Wheeler-DeWitt equation. We compute the temperature and entropy of these black holes and compare the results with the Hawking values. We observe that it is actually the noncommutativity in the momentum sector that allows for the existence of a minimum in the potential, which is the key to apply the Feynman-Hibbs procedure. It is shown that this noncommutative model generates a nonunitary dynamics that predicts a vanishing probability in the neighborhood of the singularity. This result effectively regularizes the Kantowski-Sachs singularity and generalizes a similar result, previously obtained for the case of Schwarzschild black holes.

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Section: Introductionmentioning

confidence: 99%

Noncanonical phase-space noncommutativity and the Kantowski-Sachs singularity for black holes

Bastos¹,

Bertolami

Dias

et al. 2011

Phys. Rev. D

Self Cite

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“…In terms of cosmological studies, a number of interesting noncommutativity studies have been performed in [22], [24], [65] - [67] in standard variables.…”

Section: Hamiltonian Evolution Of Black Hole Interiorsmentioning

confidence: 99%

Non-commutative black holes of various genera in the connection formalism

Schneider,

DeBenedictis

2020

Preprint

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We consider black hole interiors of arbitrary genus number within the paradigm of noncommutative geometry. The study is performed in two ways: One way is a simple smearing of a matter distribution within the black hole. The resulting structure is often known in the literature as a "model inspired by non-commutative geometry". The second method involves a more fundamental approach, in which the Hamiltonian formalism is utilized and a non-trivial Poisson bracket is introduced between the configuration degrees of freedom, as well as between the canonical momentum degrees of freedom. This is done in terms of connection variables instead of the more common ADM variables. Connection variables are utilized here since non-commutative effects are usually inspired from the quantum theory, and it is the connection variables that are used in some of the more promising modern theories of quantum gravity. We find that in the first study, the singularity of the black holes can easily be removed. In the second study, we find that introducing a non-trivial bracket between the connections (the configuration variables) may delay the singularity, but not necessarily eliminate it. However, by introducing a non-trivial bracket between the densitized triads (the canonical momentum variables) the singularity can generally be removed. In some cases, new horizons also appear due to the non-commutativity.

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“…Using the variables x, y, π x , and π y which satisfy commutative Poisson brackets (4.1), we can express the noncommutative Poisson algebra (4.10) [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]36]. Here, we develop more generic deformation of variables.…”

Section: The Classical System a Classical Commutative Solutionmentioning

confidence: 99%

“…Since the seminal paper Ref. [3] appeared, many authors have studied noncommutative quantum cosmologies [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. In the noncommutative quantum cosmological scenario, the authors considered deformation of the minisuperspace variables instead of deformation of the spacetime algebra, which is a hard task to treat neatly.…”

Section: Introductionmentioning

confidence: 99%

Accelerating cosmologies in an integrable model with noncommutative minisuperspace variables

Kan,

Kuniyasu,

Shiraishi

et al. 2019

Preprint

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We study classical and quantum noncommutative cosmology with a Liouville-type scalar degree of freedom. The noncommutativity is imposed on the minisuperspace variables through a deformation of the Poisson algebra. In this paper, we investigate the effects of noncommutativity of minisuperspace variables on the accelerating behavior of the cosmic scale factor. The probability distribution in noncommutative quantum cosmology is also studied and we propose a novel candidate for interpretation of the probability distribution in terms of noncommutative arguments.

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Noncommutative Quantum Mechanics and Quantum Cosmology

Cited by 30 publications

References 18 publications

Noncanonical phase-space noncommutativity and the Kantowski-Sachs singularity for black holes

Noncanonical phase-space noncommutativity and the Kantowski-Sachs singularity for black holes

Non-commutative black holes of various genera in the connection formalism

Accelerating cosmologies in an integrable model with noncommutative minisuperspace variables

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