Non-local, non-commutative picture in quantum mechanics and distinguished continuous canonical maps
dc.citation.epage | 353 | en_US |
dc.citation.issueNumber | 5 | en_US |
dc.citation.spage | 345 | en_US |
dc.citation.volumeNumber | 66 | en_US |
dc.contributor.author | Hakioglu, T. | en_US |
dc.date.accessioned | 2016-02-08T10:32:04Z | |
dc.date.available | 2016-02-08T10:32:04Z | |
dc.date.issued | 2002 | en_US |
dc.department | Department of Physics | en_US |
dc.description.abstract | It 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.description.provenance | Made available in DSpace on 2016-02-08T10:32:04Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 2002 | en |
dc.identifier.doi | 10.1238/Physica.Regular.066a00345 | en_US |
dc.identifier.issn | 0031-8949 | |
dc.identifier.uri | http://hdl.handle.net/11693/24630 | |
dc.language.iso | English | en_US |
dc.publisher | IOP Science | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1238/Physica.Regular.066a00345 | en_US |
dc.source.title | Physica Scripta | en_US |
dc.subject | Eigenvalues and eigenfunctions | en_US |
dc.subject | Hamiltonians | en_US |
dc.subject | Mathematical transformations | en_US |
dc.subject | Phase space methods | en_US |
dc.subject | Polynomials | en_US |
dc.subject | Non-commutative pictures | en_US |
dc.subject | Quantum theory | en_US |
dc.title | Non-local, non-commutative picture in quantum mechanics and distinguished continuous canonical maps | en_US |
dc.type | Article | en_US |
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