A Simple Signal of Noncommutative Space

Acatrinei, Ciprian Sorin

doi:10.1142/s0217732305017536

Cited by 25 publications

(26 citation statements)

References 4 publications

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“…In Ref. [15], the authors obtained classical solutions for the system described by the Hamiltonian constraint (9) in the context of a noncommutative phase-space with symplectic structure given by Eqs. (8) with {Ω, β} = θ, instead of…”

Section: A the Classical Modelmentioning

confidence: 99%

Phase-space noncommutative quantum cosmology

et al. 2008

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We present a phase-space noncommutative extension of Quantum Cosmology and study the Kantowski-Sachs (KS) cosmological model requiring that the two scale factors of the KS metric, the coordinates of the system, and their conjugate canonical momenta do not commute. Through the Arnowitt-Deser-Misner formalism, we obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system. The Seiberg-Witten map is used to transform the noncommutative equation into a commutative one, i.e. into an equation with commutative variables, which depend on the noncommutative parameters, θ and η. Numerical solutions are found both for the classical and the quantum formulations of the system. These solutions are used to characterize the dynamics and the state of the universe. From the classical solutions we obtain the behavior of quantities such as the volume expansion, the shear and the characteristic volume. However the analysis of these quantities does not lead to any restriction on the value of the noncommutative parameters, θ and η. On the other hand, for the quantum system, one can obtain, via the numerical solution of the WDW equation, the wave function of the universe both for commutative as well as for the noncommutative models. Interestingly, we find that the existence of suitable solutions of the WDW equation imposes bounds on the values of the noncommutative parameters.Moreover, the noncommutativity in the momenta leads to damping of the wave function implying that this noncommutativity can be of relevance for the selection of possible initial states of the early universe.2

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Section: A the Classical Modelmentioning

confidence: 99%

Phase-space noncommutative quantum cosmology

et al. 2008

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“…(28) forbids an electromagnetic field strength to depend only on the coordinates q. A detailed study appeared in [7]. Dimensional reduction cannot occur.…”

Section: General Resultsmentioning

confidence: 99%

Dimensional reduction for generalized Poisson brackets

Acatrinei

2008

Journal of Mathematical Physics

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“…therein]. In the one-particle sector of QFT, several noncommutative versions of quantum mechanics (NCQM) have been discussed 4,5,6,7,8,9 .…”

Section: Introductionmentioning

confidence: 99%

“…Most of these models are based on canonical extensions of the Heisenberg-Weyl algebra 6,7,8,9 . In these, time is required to be a commutative parameter and the theory lives in a 2d-dimensional phase-space of operators with noncommuting position and momentum variables.…”

Section: Introductionmentioning

confidence: 99%

Noncommutative Quantum Mechanics and Quantum Cosmology

Bastos

Bertolami

Dias

et al. 2009

Int. J. Mod. Phys. A

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We present a phase-space noncommutative version of quantum mechanics and apply this extension to Quantum Cosmology. We motivate this type of noncommutative algebra through the gravitational quantum well (GQW) where the noncommutativity between momenta is shown to be relevant. We also discuss some qualitative features of the GQW such as the Berry phase. In the context of quantum cosmology we consider a Kantowski-Sachs cosmological model and obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system through the ADM formalism and a suitable Seiberg-Witten (SW) map. The WDW equation is explicitly dependent on the noncommutative parameters, θ and η. We obtain numerical solutions of the noncommutative WDW equation for different values of the noncommutative parameters. We conclude that the noncommutativity in the momenta sector leads to a damped wave function implying that this type of noncommmutativity can be relevant for a selection of possible initial states for the universe.

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A Simple Signal of Noncommutative Space

Abstract: We propose a simple low-energy classical experiment in which the effects of noncommutativity can be clearly separated from commutative physics. The ensuing bound on the noncommutative scale is remarkable, especially in view of its elementary derivation.

Cited by 25 publications

References 4 publications

Phase-space noncommutative quantum cosmology

Phase-space noncommutative quantum cosmology

Dimensional reduction for generalized Poisson brackets

Noncommutative Quantum Mechanics and Quantum Cosmology

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