# 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…

U(1) gauge invariant noncommutative Schrödinger theory and gravity

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We consider the complex, massive Klein-Gordon field living in the noncommutative space, and coupled to noncommutative electromagnetic fields. After employing the Seiberg-Witten map to first order, we…

Can noncommutative effects account for the present speed up of the cosmic expansion

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- 2011

In this paper we investigate to which extent noncommutativity, a intrinsically quantum property, may influence the Friedmann-Robertson-Walker cosmological dynamics at late times/large scales. To our…

Noncommutative conformally coupled scalar field cosmology and its commutative counterpart

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- 2005

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…

The Quantum Potential in Gravity and Cosmology

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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…

INVERSE SQUARE PROBLEM AND so(2, 1) SYMMETRY IN NONCOMMUTATIVE SPACE

- 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,…

Covariant canonical quantization of fields and Bohmian mechanics

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- 2004

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…

The Harmonic Oscillator Influenced by Gravitational Wave in Noncommutative Quantum Phase Space

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- 2014

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…

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