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dc.contributor.authorHakioglu, T.en_US
dc.date.accessioned2016-02-08T10:32:04Z
dc.date.available2016-02-08T10:32:04Z
dc.date.issued2002en_US
dc.identifier.issn0031-8949
dc.identifier.urihttp://hdl.handle.net/11693/24630
dc.description.abstractIt is shown that continuous classical nonlinear canonical (Poisson) maps have a distinguished role in quantum mechanics. They act unitarily on the quantum phase space and generate h-independent quantum nonlinear canonical maps. It is also shown that such maps act in the non-commutative phase space under the classical covariance. A crucial result of the work is that under the action of Poisson maps a local quantum mechanical picture is converted onto a non-local picture which is then represented in a non-local Hilbert space. On the other hand, it is known that a non-local picture is equivalent by the Weyl map to a non-commutative picture which, in the context of this work, corresponds to a phase space formulation of the theory. As a result of this equivalence, a phase space Schrödinger picture can be formulated. In particular, we obtain the *-genvalue equation of Fairlie [Proc. Camb. Phil. Soc., 60, 581 (1964)] and Curtright, Fairlie and Zachos [Phys. Rev., D 58, 025002 (1998)]. In a non-local picture entanglement becomes a crucial concept. The connection between the entanglement and non-locality is explored in the context of Poisson maps and specific examples of the generation of entanglement from a local wavefunction are provided by using the concept of generalized Bell states. The results obtained are also relevant for the non-commutative soliton picture in the non-commutative field theories. We elaborate on this in the context of the scalar non-commutative field theory.en_US
dc.language.isoEnglishen_US
dc.source.titlePhysica Scriptaen_US
dc.relation.isversionofhttp://dx.doi.org/10.1238/Physica.Regular.066a00345en_US
dc.subjectEigenvalues and eigenfunctionsen_US
dc.subjectHamiltoniansen_US
dc.subjectMathematical transformationsen_US
dc.subjectPhase space methodsen_US
dc.subjectPolynomialsen_US
dc.subjectNon-commutative picturesen_US
dc.subjectQuantum theoryen_US
dc.titleNon-local, non-commutative picture in quantum mechanics and distinguished continuous canonical mapsen_US
dc.typeArticleen_US
dc.departmentDepartment of Physics
dc.citation.spage345en_US
dc.citation.epage353en_US
dc.citation.volumeNumber66en_US
dc.citation.issueNumber5en_US
dc.identifier.doi10.1238/Physica.Regular.066a00345en_US
dc.publisherIOP Scienceen_US


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