Categorical Operator Algebraic Foundations of Relational Quantum Theory

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 in...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2014-12
Main Author: Bertozzini, Paolo
Format: Article
Language:English
Subjects:
Algebra
Operators (mathematics)
Quantum gravity
Quantum theory
Relativity
Spacetime
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Bertozzini, Paolo
description 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 article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2085052874</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2085052874</sourcerecordid><originalsourceid>FETCH-proquest_journals_20850528743</originalsourceid><addsrcrecordid>eNqNi8sKgkAUQIcgSMp_GGgtTHecdBuStYvCfUx2NWXy2jwW_X0SfUCrw4FzZiwCKTdJngIsWOxcL4SAbQZKyYgdCu2xJdvV2vDTiFZ7snxnWrxZ3dW8pDDcte9ocJwafkHzlSk-Bz348OTVA8m-V2zeaOMw_nHJ1uW-Ko7JaOkV0PlrT8FOn7uCyJVQkGep_K_6ACQ0O_I</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2085052874</pqid></control><display><type>article</type><title>Categorical Operator Algebraic Foundations of Relational Quantum Theory</title><source>Publicly Available Content (ProQuest)</source><creator>Bertozzini, Paolo</creator><creatorcontrib>Bertozzini, Paolo</creatorcontrib><description>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.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Algebra ; Operators (mathematics) ; Quantum gravity ; Quantum theory ; Relativity ; Spacetime</subject><ispartof>arXiv.org, 2014-12</ispartof><rights>2014. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2085052874?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>780,784,25753,37012,44590</link.rule.ids></links><search><creatorcontrib>Bertozzini, Paolo</creatorcontrib><title>Categorical Operator Algebraic Foundations of Relational Quantum Theory</title><title>arXiv.org</title><description>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.</description><subject>Algebra</subject><subject>Operators (mathematics)</subject><subject>Quantum gravity</subject><subject>Quantum theory</subject><subject>Relativity</subject><subject>Spacetime</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNqNi8sKgkAUQIcgSMp_GGgtTHecdBuStYvCfUx2NWXy2jwW_X0SfUCrw4FzZiwCKTdJngIsWOxcL4SAbQZKyYgdCu2xJdvV2vDTiFZ7snxnWrxZ3dW8pDDcte9ocJwafkHzlSk-Bz348OTVA8m-V2zeaOMw_nHJ1uW-Ko7JaOkV0PlrT8FOn7uCyJVQkGep_K_6ACQ0O_I</recordid><startdate>20141223</startdate><enddate>20141223</enddate><creator>Bertozzini, Paolo</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20141223</creationdate><title>Categorical Operator Algebraic Foundations of Relational Quantum Theory</title><author>Bertozzini, Paolo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_20850528743</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Algebra</topic><topic>Operators (mathematics)</topic><topic>Quantum gravity</topic><topic>Quantum theory</topic><topic>Relativity</topic><topic>Spacetime</topic><toplevel>online_resources</toplevel><creatorcontrib>Bertozzini, Paolo</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content (ProQuest)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bertozzini, Paolo</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Categorical Operator Algebraic Foundations of Relational Quantum Theory</atitle><jtitle>arXiv.org</jtitle><date>2014-12-23</date><risdate>2014</risdate><eissn>2331-8422</eissn><abstract>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.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2014-12
issn 2331-8422
language eng
recordid cdi_proquest_journals_2085052874
source Publicly Available Content (ProQuest)
subjects Algebra
Operators (mathematics)
Quantum gravity
Quantum theory
Relativity
Spacetime
title Categorical Operator Algebraic Foundations of Relational Quantum Theory
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-05T09%3A29%3A20IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Categorical%20Operator%20Algebraic%20Foundations%20of%20Relational%20Quantum%20Theory&rft.jtitle=arXiv.org&rft.au=Bertozzini,%20Paolo&rft.date=2014-12-23&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E2085052874%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-proquest_journals_20850528743%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2085052874&rft_id=info:pmid/&rfr_iscdi=true