# Noncommutative quantum mechanics and Bohm's ontological interpretation

@article{Barbosa2004NoncommutativeQM, title={Noncommutative quantum mechanics and Bohm's ontological interpretation}, author={G. D. Barbosa and N. Pinto-Neto}, journal={Physical Review D}, year={2004}, volume={69}, pages={065014} }

We carry out an investigation into the possibility of developing a Bohmian interpretation based on the continuous motion of point particles for noncommutative quantum mechanics. The conditions for such an interpretation to be consistent are determined, and the implications of its adoption for noncommutativity are discussed. A Bohmian analysis of the noncommutative harmonic oscillator is carried out in detail. By studying the particle motion in the oscillator orbits, we show that small-scale…

## 16 Citations

Noncommutative geometry and cosmology

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We study some consequences of noncommutativity to homogeneous cosmologies by introducing a deformation of the commutation relation between the minisuperspace variables. The investigation is carried…

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- 2011

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We study the implications of a noncommutative geometry of the minisuperspace variables for the Friedmann-Robertson-Walker universe with a conformally coupled scalar field. The investigation is…

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- 2006

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- 2014

The fundamental role of Bohm’s quantum potential in the treatment of gravity and thus in the general-relativistic domain has been explored by various authors (see, for example, the book of R. Carroll…

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- Physics, Mathematics
- 2009

We study the quantum mechanics of a system with inverse square potential in noncommutative space. Both the coordinates and momenta are considered to be noncommutative, which breaks the original so(2,…

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Abstract.We propose a manifestly covariant canonical method of field quantization based on the classical De Donder-Weyl covariant canonical formulation of field theory. Owing to covariance, the space…

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- 2008

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Dynamical property of harmonic oscillator affected by linearized gravitational wave (LGW) is studied in a particular case of both position and momentum operators which are noncommutative to each…

## References

SHOWING 1-10 OF 63 REFERENCES

Noncommutative quantum mechanics and rotating frames

- Physics
- 2002

We study the effect of noncommutativity of space on the physics of a quantum interferometer located in a rotating disk in a gauge field background. To this end, we develop a path-integral approach…

A NOVEL APPROACH TO NONCOMMUTATIVITY IN PLANAR QUANTUM MECHANICS

- Physics
- 2001

Noncommutative algebra in planar quantum mechanics is shown to follow from 't Hooft's recent analysis on dissipation and quantization. The noncommutativity in the coordinates or in the momenta of a…

Noncommutative quantum cosmology.

- Physics, MedicinePhysical review letters
- 2002

It is shown that new quantum states that "compete" to be the most probable state appear, in clear contrast with the commutative case, in the noncommutative quantum cosmology model.

On the Meaning of the String-Inspired Noncommutativity and its Implications

- Physics
- 2003

We propose an alternative interpretation for the meaning of noncommutativity of the string-inspired field theories and quantum mechanics. Arguments are presented to show that the noncommutativity…

Noncommutative quantum mechanics from noncommutative quantum field theory.

- Physics, MedicinePhysical review letters
- 2002

We derive noncommutative multiparticle quantum mechanics from noncommutative quantum field theory in the nonrelativistic limit. Particles of opposite charges are found to have opposite…

Quantum theories on noncommutative spaces with nontrivial topology: Aharonov-Bohm and Casimir effects

- Physics
- 2001

Abstract After discussing the peculiarities of quantum systems on noncommutative (NC) spaces with nontrivial topology and the operator representation of the ★-product on them, we consider the…

Quantum mechanics on the noncommutative plane and sphere

- Physics
- 2001

Abstract 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…

Quantum Mechanics on the Noncommutative Torus

- Physics
- 2001

We analyze the algebra of observables of a charged particle on a noncommutative torus in a constant magnetic field. We present a set of generators of this algebra which coincide with the generators…

Noncommutative perturbative dynamics

- Physics
- 2000

We study the perturbative dynamics of noncommutative field theories on R d , and find an intriguing mixing of the UV and the IR. High energies of virtual particles in loops produce non-analyticity at…

Noncommutative field theory and Lorentz violation.

- Physics, MedicinePhysical review letters
- 2001

Any realistic noncommutative theory is found to be physically equivalent to a subset of a general Lorentz-violating standard-model extension involving ordinary fields.