Categorical Operator Algebraic Foundations of Relational Quantum Theory
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arXiv
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| Format: | Preprint |
| Publié: |
2014
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| _version_ | 1866918162006540288 |
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| author | Bertozzini, Paolo |
| author_facet | Bertozzini, Paolo |
| contents | We provide an algebraic formulation of C.Rovelli's relational quantum theory that is based on suitable notions of "non-commutative" higher operator categories, originally developed in the study of categorical non-commutative geometry. As a way to implement C.Rovelli's original intuition on the relational origin of space-time, in the context of our proposed algebraic approach to quantum gravity via Tomita-Takesaki modular theory, we tentatively suggest to use this categorical formalism in order to spectrally reconstruct non-commutative relational space-time geometries from categories of correlation bimodules between operator algebras of observables. Parts of this work are joint collaborations with: Dr.Roberto Conti (Sapienza Universita' di Roma), Assoc.Prof.Wicharn Lewkeeratiyutkul (Chulalongkorn University, Bangkok), Dr.Rachel Dawe Martins (Istituto Superior Tecnico, Lisboa), Dr.Matti Raasakka (Paris 13 University), Dr.Noppakhun Suthichitranont. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1412_7256 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Categorical Operator Algebraic Foundations of Relational Quantum Theory Bertozzini, Paolo Mathematical Physics Category Theory Quantum Physics 81P99, 18D05, 46L89, 46M15 We provide an algebraic formulation of C.Rovelli's relational quantum theory that is based on suitable notions of "non-commutative" higher operator categories, originally developed in the study of categorical non-commutative geometry. As a way to implement C.Rovelli's original intuition on the relational origin of space-time, in the context of our proposed algebraic approach to quantum gravity via Tomita-Takesaki modular theory, we tentatively suggest to use this categorical formalism in order to spectrally reconstruct non-commutative relational space-time geometries from categories of correlation bimodules between operator algebras of observables. Parts of this work are joint collaborations with: Dr.Roberto Conti (Sapienza Universita' di Roma), Assoc.Prof.Wicharn Lewkeeratiyutkul (Chulalongkorn University, Bangkok), Dr.Rachel Dawe Martins (Istituto Superior Tecnico, Lisboa), Dr.Matti Raasakka (Paris 13 University), Dr.Noppakhun Suthichitranont. |
| title | Categorical Operator Algebraic Foundations of Relational Quantum Theory |
| topic | Mathematical Physics Category Theory Quantum Physics 81P99, 18D05, 46L89, 46M15 |
| url | https://arxiv.org/abs/1412.7256 |