Noncommutative quantum mechanics

Gamboa, J.; Loewe, M.; Rojas, J. C.

doi:10.1103/physrevd.64.067901

Cited by 418 publications

(360 citation statements)

References 19 publications

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“…Quantum mechanics on the noncommutative plane can be defined in terms of a projection to the lowest Landau level of dynamics on the commuting plane; some features of this were contained in [4]. The case of a central potential on the noncommutative plane was recently discussed in [5]. In this paper, we will analyze the algebraic structures in more detail.…”

Section: Introductionmentioning

confidence: 99%

Quantum mechanics on the noncommutative plane and sphere

Nair¹,

2001

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We consider the quantum mechanics of a particle on a noncommutative plane. The case of a charged particle in a magnetic field (the Landau problem) with a harmonic oscillator potential is solved. There is a critical point with the density of states becoming infinite for the value of the magnetic field equal to the inverse of the noncommutativity parameter.The Landau problem on the noncommutative two-sphere is also solved and compared to the plane problem.

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Section: Introductionmentioning

confidence: 99%

Quantum mechanics on the noncommutative plane and sphere

Nair¹,

2001

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“…In particular, Compean et al, (Compean et al,2002(Compean et al, ,2003a avoid the difficult technicalities of analyzing noncommutative cosmological models, when these are derived from the full noncommutative theory of gravity, see by example (Bañados et al, 2001;Nishino-Rajpoot,2002;,hep-th/0203038; Abe-Nair,hep-th/0212270; Cardella-Zanon,hep-th/0212071; Chaichian et al, 2001), their proposal is to introduce the effects of noncommutativity in quantum cosmology including one θ parameter, deforming the minisuperspace. This deformation is achieved through a Moyal deformation of the Wheeler-DeWitt (WDW) equation, this is similar to noncommutative quantum mechanics (Gamboa, 2001;Chaichian et al, 2001). Some work has been done in this direction, for example in (Barbosa-2005) the authors study the implications of noncommutative geometry in minisuperspace variables for a FRW universe with a conformally coupled scalar field, using the bohmian formalism of quantum trajectories (Barbosa, 2004) also in (Pimentel, 2005) a noncommutative deformation of a scalar field coupled to scalar-tensor type gravity was considered.…”

Section: Introductionmentioning

confidence: 99%

Noncommutative Bianchi Type II Quantum Cosmology

et al. 2007

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In this paper we present the noncommutative Bianchi Class A cosmological models coupled to barotropic perfect fluid. The commutative and noncommutative quantum solution to the Wheeler-DeWitt equation for any factor ordering, to the anisotropic Bianchi type II cosmological model are found, using a stiff fluid (γ = 1). In our toy model, we introduce noncommutative scale factors, is say, we consider that all minisuperspace variables q i does not commute, so the simplectic structure was modified.

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“…it has been shown elsewhere [4][5][6] that the time evolution of the system, in the Schrödinger picture, is described by the wave equation…”

Section: Classical-quantum Transition For Noncommutative Systemsmentioning

confidence: 99%

“…In Refs. [3][4][5][6][7] the reader will find specific examples of noncommutative systems whose quantization has been successfully carried out. While Ref.…”

Section: Introductionmentioning

confidence: 99%

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On the quantum dynamics of non-commutative systems

Bemfica¹,

Girotti²

2008

Braz. J. Phys.

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This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and quantum dynamics for the models under investigation. We then elaborate on recently reported results concerned with the sufficient conditions for the existence of the Born series and unitarity and turn, afterwards, into analyzing the functional quantization of non-commutative systems. The compatibility between the operator and the functional approaches is established in full generality. The intricacies arising in connection with the explicit computation of path integrals, for the systems under scrutiny, is illustrated by presenting the detailed calculation of the Feynman kernel for the non-commutative two dimensional harmonic oscillator.

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Noncommutative quantum mechanics

Cited by 418 publications

References 19 publications

Quantum mechanics on the noncommutative plane and sphere

Quantum mechanics on the noncommutative plane and sphere

Noncommutative Bianchi Type II Quantum Cosmology

On the quantum dynamics of non-commutative systems

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