On the Mass Dependence of the Modular Operator for a Double Cone
We present a numerical approximation scheme for the Tomita–Takesaki modular operator of local subalgebras in linear quantum fields, working at one-particle level. This is applied to the local subspaces for double cones in the vacuum sector of a massive scalar free field in ( 1 + 1 ) - and ( 3 + 1 )...
Gespeichert in:
| Veröffentlicht in: | Annales Henri Poincaré 2023-09, Vol.24 (9), p.3031-3054 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 3054 |
|---|---|
| container_issue | 9 |
| container_start_page | 3031 |
| container_title | Annales Henri Poincaré |
| container_volume | 24 |
| creator | Bostelmann, Henning Cadamuro, Daniela Minz, Christoph |
| description | We present a numerical approximation scheme for the Tomita–Takesaki modular operator of local subalgebras in linear quantum fields, working at one-particle level. This is applied to the local subspaces for double cones in the vacuum sector of a massive scalar free field in
(
1
+
1
)
- and
(
3
+
1
)
-dimensional Minkowski spacetime, using a discretization of time-0 data in position space. In the case of a wedge region, one component of the modular generator is well known to be a mass-independent multiplication operator; our results strongly suggest that for the double cone, the corresponding component is still at least close to a multiplication operator, but that it is dependent on mass and angular momentum. |
| doi_str_mv | 10.1007/s00023-023-01311-3 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2842544992</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2842544992</sourcerecordid><originalsourceid>FETCH-LOGICAL-c363t-c1ecdc5fdc4b2a7029c89f753039bde83f13fcda0677adbb7cb565ba74f502ea3</originalsourceid><addsrcrecordid>eNp9kEtPwzAQhC0EEqXwBzhZ4hxYPxInN1DLSyrqBc6WH2ugKnGwkwP_nrRBcOMw2tVqZlb6CDlncMkA1FUGAC6KvZhgrBAHZMYklwVUFTv83YU6Jic5bwAYr0UzI9frlvZvSJ9MznSJHbYeW4c0hukc_bA1ia47TKaPiYZRhi7jYLdIF7HFU3IUzDbj2c-ck5e72-fFQ7Fa3z8ublaFE5XoC8fQeVcG76TlRgFvXN0EVQoQjfVYi8BEcN5ApZTx1ipny6q0RslQAkcj5uRi6u1S_Bww93oTh9SOLzWvJS-lbBo-uvjkcinmnDDoLr1_mPSlGegdKT2R0nvtSGkxhsQUyqO5fcX0V_1P6hvd-Wpy</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2842544992</pqid></control><display><type>article</type><title>On the Mass Dependence of the Modular Operator for a Double Cone</title><source>SpringerLink Journals - AutoHoldings</source><creator>Bostelmann, Henning ; Cadamuro, Daniela ; Minz, Christoph</creator><creatorcontrib>Bostelmann, Henning ; Cadamuro, Daniela ; Minz, Christoph</creatorcontrib><description>We present a numerical approximation scheme for the Tomita–Takesaki modular operator of local subalgebras in linear quantum fields, working at one-particle level. This is applied to the local subspaces for double cones in the vacuum sector of a massive scalar free field in
(
1
+
1
)
- and
(
3
+
1
)
-dimensional Minkowski spacetime, using a discretization of time-0 data in position space. In the case of a wedge region, one component of the modular generator is well known to be a mass-independent multiplication operator; our results strongly suggest that for the double cone, the corresponding component is still at least close to a multiplication operator, but that it is dependent on mass and angular momentum.</description><identifier>ISSN: 1424-0637</identifier><identifier>EISSN: 1424-0661</identifier><identifier>DOI: 10.1007/s00023-023-01311-3</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Angular momentum ; Classical and Quantum Gravitation ; Dynamical Systems and Ergodic Theory ; Elementary Particles ; Mathematical analysis ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Minkowski space ; Operators (mathematics) ; Physics ; Physics and Astronomy ; Quantum Field Theory ; Quantum Physics ; Relativity Theory ; Subspaces ; Theoretical</subject><ispartof>Annales Henri Poincaré, 2023-09, Vol.24 (9), p.3031-3054</ispartof><rights>The Author(s) 2023</rights><rights>The Author(s) 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c363t-c1ecdc5fdc4b2a7029c89f753039bde83f13fcda0677adbb7cb565ba74f502ea3</citedby><cites>FETCH-LOGICAL-c363t-c1ecdc5fdc4b2a7029c89f753039bde83f13fcda0677adbb7cb565ba74f502ea3</cites><orcidid>0000-0002-0233-2928 ; 0000-0002-8639-9731 ; 0000-0002-5429-5997</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00023-023-01311-3$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00023-023-01311-3$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Bostelmann, Henning</creatorcontrib><creatorcontrib>Cadamuro, Daniela</creatorcontrib><creatorcontrib>Minz, Christoph</creatorcontrib><title>On the Mass Dependence of the Modular Operator for a Double Cone</title><title>Annales Henri Poincaré</title><addtitle>Ann. Henri Poincaré</addtitle><description>We present a numerical approximation scheme for the Tomita–Takesaki modular operator of local subalgebras in linear quantum fields, working at one-particle level. This is applied to the local subspaces for double cones in the vacuum sector of a massive scalar free field in
(
1
+
1
)
- and
(
3
+
1
)
-dimensional Minkowski spacetime, using a discretization of time-0 data in position space. In the case of a wedge region, one component of the modular generator is well known to be a mass-independent multiplication operator; our results strongly suggest that for the double cone, the corresponding component is still at least close to a multiplication operator, but that it is dependent on mass and angular momentum.</description><subject>Angular momentum</subject><subject>Classical and Quantum Gravitation</subject><subject>Dynamical Systems and Ergodic Theory</subject><subject>Elementary Particles</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Minkowski space</subject><subject>Operators (mathematics)</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Field Theory</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Subspaces</subject><subject>Theoretical</subject><issn>1424-0637</issn><issn>1424-0661</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kEtPwzAQhC0EEqXwBzhZ4hxYPxInN1DLSyrqBc6WH2ugKnGwkwP_nrRBcOMw2tVqZlb6CDlncMkA1FUGAC6KvZhgrBAHZMYklwVUFTv83YU6Jic5bwAYr0UzI9frlvZvSJ9MznSJHbYeW4c0hukc_bA1ia47TKaPiYZRhi7jYLdIF7HFU3IUzDbj2c-ck5e72-fFQ7Fa3z8ublaFE5XoC8fQeVcG76TlRgFvXN0EVQoQjfVYi8BEcN5ApZTx1ipny6q0RslQAkcj5uRi6u1S_Bww93oTh9SOLzWvJS-lbBo-uvjkcinmnDDoLr1_mPSlGegdKT2R0nvtSGkxhsQUyqO5fcX0V_1P6hvd-Wpy</recordid><startdate>20230901</startdate><enddate>20230901</enddate><creator>Bostelmann, Henning</creator><creator>Cadamuro, Daniela</creator><creator>Minz, Christoph</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-0233-2928</orcidid><orcidid>https://orcid.org/0000-0002-8639-9731</orcidid><orcidid>https://orcid.org/0000-0002-5429-5997</orcidid></search><sort><creationdate>20230901</creationdate><title>On the Mass Dependence of the Modular Operator for a Double Cone</title><author>Bostelmann, Henning ; Cadamuro, Daniela ; Minz, Christoph</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-c1ecdc5fdc4b2a7029c89f753039bde83f13fcda0677adbb7cb565ba74f502ea3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Angular momentum</topic><topic>Classical and Quantum Gravitation</topic><topic>Dynamical Systems and Ergodic Theory</topic><topic>Elementary Particles</topic><topic>Mathematical analysis</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Minkowski space</topic><topic>Operators (mathematics)</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Field Theory</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Subspaces</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bostelmann, Henning</creatorcontrib><creatorcontrib>Cadamuro, Daniela</creatorcontrib><creatorcontrib>Minz, Christoph</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Annales Henri Poincaré</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bostelmann, Henning</au><au>Cadamuro, Daniela</au><au>Minz, Christoph</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Mass Dependence of the Modular Operator for a Double Cone</atitle><jtitle>Annales Henri Poincaré</jtitle><stitle>Ann. Henri Poincaré</stitle><date>2023-09-01</date><risdate>2023</risdate><volume>24</volume><issue>9</issue><spage>3031</spage><epage>3054</epage><pages>3031-3054</pages><issn>1424-0637</issn><eissn>1424-0661</eissn><abstract>We present a numerical approximation scheme for the Tomita–Takesaki modular operator of local subalgebras in linear quantum fields, working at one-particle level. This is applied to the local subspaces for double cones in the vacuum sector of a massive scalar free field in
(
1
+
1
)
- and
(
3
+
1
)
-dimensional Minkowski spacetime, using a discretization of time-0 data in position space. In the case of a wedge region, one component of the modular generator is well known to be a mass-independent multiplication operator; our results strongly suggest that for the double cone, the corresponding component is still at least close to a multiplication operator, but that it is dependent on mass and angular momentum.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00023-023-01311-3</doi><tpages>24</tpages><orcidid>https://orcid.org/0000-0002-0233-2928</orcidid><orcidid>https://orcid.org/0000-0002-8639-9731</orcidid><orcidid>https://orcid.org/0000-0002-5429-5997</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1424-0637 |
| ispartof | Annales Henri Poincaré, 2023-09, Vol.24 (9), p.3031-3054 |
| issn | 1424-0637 1424-0661 |
| language | eng |
| recordid | cdi_proquest_journals_2842544992 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Angular momentum Classical and Quantum Gravitation Dynamical Systems and Ergodic Theory Elementary Particles Mathematical analysis Mathematical and Computational Physics Mathematical Methods in Physics Minkowski space Operators (mathematics) Physics Physics and Astronomy Quantum Field Theory Quantum Physics Relativity Theory Subspaces Theoretical |
| title | On the Mass Dependence of the Modular Operator for a Double Cone |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-12T10%3A39%3A23IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20the%20Mass%20Dependence%20of%20the%20Modular%20Operator%20for%20a%20Double%20Cone&rft.jtitle=Annales%20Henri%20Poincar%C3%A9&rft.au=Bostelmann,%20Henning&rft.date=2023-09-01&rft.volume=24&rft.issue=9&rft.spage=3031&rft.epage=3054&rft.pages=3031-3054&rft.issn=1424-0637&rft.eissn=1424-0661&rft_id=info:doi/10.1007/s00023-023-01311-3&rft_dat=%3Cproquest_cross%3E2842544992%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2842544992&rft_id=info:pmid/&rfr_iscdi=true |