Noncommutative quantum mechanics and Bohm’s ontological interpretation

Barbosa, G. D.; Pinto-Neto, Nelson

doi:10.1103/physrevd.69.065014

Cited by 22 publications

(21 citation statements)

References 63 publications

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“…A version of the Bohmian interpretation of relativistic particles might be indirectly testable even with near-future technology [18]. The Bohmian interpretation has also been proposed as a possible interpretation of noncommutative QM [19]. Using our results on the manifestly covariant canonical quantization of fields [20,21], we have recently argued [22] that the natural formulation of strings compatible with the world-sheet covariance on the quantum level is, indeed, a formulation in terms of Bohmian deterministic hidden variables.…”

Section: Introductionmentioning

confidence: 99%

Strings, T-duality breaking, and nonlocality without the shortest distance

Nikolić

2007

Eur. Phys. J. C

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T-duality of string theory suggests nonlocality manifested as the shortest possible distance. As an alternative, we suggest a nonlocal formulation of string theory that breaks T-duality at the fundamental level and does not require the shortest possible distance. Instead, the string has an objective shape in spacetime at all length scales, but different parts of the string interact in a nonlocal Bohmian manner.

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Section: Introductionmentioning

confidence: 99%

Strings, T-duality breaking, and nonlocality without the shortest distance

Nikolić

2007

Eur. Phys. J. C

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“…This, together with the results of [18,19] related to relativistic first quantization, suggests that it is Bohmian mechanics that might be the missing bridge between quantum mechanics and relativity. In addition, we also note that the Bohmian interpretation might play an important role for quantum cosmology [20,21,22,23,24] and noncommutative theories [25].…”

Section: Introductionmentioning

confidence: 99%

Covariant canonical quantization of fields and Bohmian mechanics

Nikolić

2005

Eur. Phys. J. C

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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 and time arguments of fields are treated on an equal footing. To achieve both covariance and consistency with standard noncovariant canonical quantization of fields in Minkowski spacetime, it is necessary to adopt a covariant Bohmian formulation of quantum field theory. A preferred foliation of spacetime emerges dynamically owing to a purely quantum effect. The application to a simple time-reparametrization invariant system and quantum gravity is discussed and compared with the conventional noncovariant WheelerDeWitt approach.

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“…We could try to further argue that both the old and new space-time operators are observables and that θ reflects the noncommutativity of the old observables. This, however, brings in a somewhat Bohmian flavor of hidden variables to the new quantization which is, to say the least, subject to questioning (for additional arguments regarding this issue see [16]). Thus, from our point of view, it would seem preferable to conclude that in the case of the quantizations discussed in subsection 4.1.4, the term "space-time noncommutativity" is a misnomer.…”

Section: Discussionmentioning

confidence: 99%

Noncommutativity from canonical and noncanonical structures

Rosenbaum¹,

Vergara²,

Juárez³

2008

Non-Commutative Geometry in Mathematics and Physics

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Abstract. Using arbitrary symplectic structures and parametrization invariant actions, we develop a formalism, based on Dirac's quantization procedure, that allows us to consider theories with both space-space as well as space-time noncommutativity. Because the formalism has as a starting point an action, the procedure admits quantizing the theory either by obtaining the quantum evolution equations or by using the path integral techniques. For both approaches we only need to select a complete basis of commutative observables. We show that for certain choices of the potentials that generate a given symplectic structure, the phase of the quantum transition function between the admissible bases corresponds to a linear canonical transformation, by means of which the actions associated to each of these bases may be related and hence lead to equivalent quantizations. There are however other potentials that result in actions which can not be related to the previous ones by canonical transformations, and for which the fixed end-points, in terms of the admissible bases, can only be realized by means of a Darboux map. In such cases the original arbitrary symplectic structure is reduced to its canonical form and therefore each of these actions results in a different quantum theory. One interesting feature of the formalism here discussed is that it can be introduced both at the levels of particle systems as well as of field theory.

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Noncommutative quantum mechanics and Bohm’s ontological interpretation

Cited by 22 publications

References 63 publications

Strings, T-duality breaking, and nonlocality without the shortest distance

Strings, T-duality breaking, and nonlocality without the shortest distance

Covariant canonical quantization of fields and Bohmian mechanics

Noncommutativity from canonical and noncanonical structures

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