Geometric Quantization and Epistemically Restricted Theories: The Continuous Case
It is possible to reproduce the quantum features of quantum states, starting from a classical statistical theory and then limiting the amount of knowledge that an agent can have about an individual system [5, 18].These are so called epistemic restrictions. Such restrictions have been recently formul...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Open Publishing Association
2017-01-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1603.02189v3 |
| _version_ | 1818519442077777920 |
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| author | Ivan Contreras Ali Nabi Duman |
| author_facet | Ivan Contreras Ali Nabi Duman |
| author_sort | Ivan Contreras |
| collection | DOAJ |
| description | It is possible to reproduce the quantum features of quantum states, starting from a classical statistical theory and then limiting the amount of knowledge that an agent can have about an individual system [5, 18].These are so called epistemic restrictions. Such restrictions have been recently formulated in terms of the symplectic geometry of the corresponding classical theory [19]. The purpose of this note is to describe, using this symplectic framework, how to obtain a C*-algebraic formulation for the epistemically restricted theories. In the case of continuous variables, following the groupoid quantization recipe of E. Hawkins, we obtain a twisted group C*-algebra which is the usual Moyal quantization of a Poisson vector space [12]. |
| first_indexed | 2024-12-11T01:24:16Z |
| format | Article |
| id | doaj.art-f3bc2f1e026d4a55a233b9218d7258a4 |
| institution | Directory Open Access Journal |
| issn | 2075-2180 |
| language | English |
| last_indexed | 2024-12-11T01:24:16Z |
| publishDate | 2017-01-01 |
| publisher | Open Publishing Association |
| record_format | Article |
| series | Electronic Proceedings in Theoretical Computer Science |
| spelling | doaj.art-f3bc2f1e026d4a55a233b9218d7258a42022-12-22T01:25:37ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802017-01-01236Proc. QPL 2016405010.4204/EPTCS.236.3:5Geometric Quantization and Epistemically Restricted Theories: The Continuous CaseIvan Contreras0Ali Nabi Duman1 University of Illinois at Urbana-Champain King Fahd University of Petroleum and Minerals It is possible to reproduce the quantum features of quantum states, starting from a classical statistical theory and then limiting the amount of knowledge that an agent can have about an individual system [5, 18].These are so called epistemic restrictions. Such restrictions have been recently formulated in terms of the symplectic geometry of the corresponding classical theory [19]. The purpose of this note is to describe, using this symplectic framework, how to obtain a C*-algebraic formulation for the epistemically restricted theories. In the case of continuous variables, following the groupoid quantization recipe of E. Hawkins, we obtain a twisted group C*-algebra which is the usual Moyal quantization of a Poisson vector space [12].http://arxiv.org/pdf/1603.02189v3 |
| spellingShingle | Ivan Contreras Ali Nabi Duman Geometric Quantization and Epistemically Restricted Theories: The Continuous Case Electronic Proceedings in Theoretical Computer Science |
| title | Geometric Quantization and Epistemically Restricted Theories: The Continuous Case |
| title_full | Geometric Quantization and Epistemically Restricted Theories: The Continuous Case |
| title_fullStr | Geometric Quantization and Epistemically Restricted Theories: The Continuous Case |
| title_full_unstemmed | Geometric Quantization and Epistemically Restricted Theories: The Continuous Case |
| title_short | Geometric Quantization and Epistemically Restricted Theories: The Continuous Case |
| title_sort | geometric quantization and epistemically restricted theories the continuous case |
| url | http://arxiv.org/pdf/1603.02189v3 |
| work_keys_str_mv | AT ivancontreras geometricquantizationandepistemicallyrestrictedtheoriesthecontinuouscase AT alinabiduman geometricquantizationandepistemicallyrestrictedtheoriesthecontinuouscase |