Aspects of the functional renormalisation group
We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A simple equation for the flow of these relations is provided....
Gespeichert in:
| Veröffentlicht in: | Annals of physics 2007-12, Vol.322 (12), p.2831-2915 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 2915 |
|---|---|
| container_issue | 12 |
| container_start_page | 2831 |
| container_title | Annals of physics |
| container_volume | 322 |
| creator | Pawlowski, Jan M. |
| description | We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A simple equation for the flow of these relations is provided. The setting includes general flows in the presence of composite operators and their relation to standard flows, an important example being NPI quantities. We discuss optimisation and derive a functional optimisation criterion. Applications deal with the interrelation between functional flows and the quantum equations of motion, general Dyson–Schwinger equations. We discuss the combined use of these functional equations as well as outlining the construction of practical renormalisation schemes, also valid in the presence of composite operators. Furthermore, the formalism is used to derive various representations of modified symmetry relations in gauge theories, as well as to discuss gauge-invariant flows. We close with the construction and analysis of truncation schemes in view of practical optimisation. |
| doi_str_mv | 10.1016/j.aop.2007.01.007 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_osti_</sourceid><recordid>TN_cdi_osti_scitechconnect_21077666</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0003491607000097</els_id><sourcerecordid>3711603161</sourcerecordid><originalsourceid>FETCH-LOGICAL-c446t-a14ac5f14f5f33215f8e2fc5ea8ded9aa629b8a8c44245da74fe4987c4b94f153</originalsourceid><addsrcrecordid>eNp9kEtLxDAUhYMoOI7-AHdF1625eTXF1TD4ggE3Cu5CJk2clpmmJq3gvzelLgTB1YHLdy4fB6FLwAVgEDdtoX1fEIzLAkOR4ggtAFcix5S_HaMFxpjmrAJxis5ibDEGYFwu0M0q9tYMMfMuG3Y2c2NnhsZ3ep8F2_lw0Psm6umSvQc_9ufoxOl9tBc_uUSv93cv68d88_zwtF5tcsOYGHINTBvugDnuKCXAnbTEGW61rG1daS1ItZVaJpowXuuSOcsqWRq2rZgDTpfoev7r49CoaJrBmp3xXZdkFQFclkKIRF3NVB_8x2jjoFo_hiQfFaFcclmyX6_-QiBkSQmhtEoUzJQJPsZgnepDc9DhSwFW08SqVWliNU2sMKgUqXM7d2xa4rOxYRK1nbF1EybP2jf_tL8B5PyCIA</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1687322339</pqid></control><display><type>article</type><title>Aspects of the functional renormalisation group</title><source>ScienceDirect Journals (5 years ago - present)</source><creator>Pawlowski, Jan M.</creator><creatorcontrib>Pawlowski, Jan M.</creatorcontrib><description>We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A simple equation for the flow of these relations is provided. The setting includes general flows in the presence of composite operators and their relation to standard flows, an important example being NPI quantities. We discuss optimisation and derive a functional optimisation criterion. Applications deal with the interrelation between functional flows and the quantum equations of motion, general Dyson–Schwinger equations. We discuss the combined use of these functional equations as well as outlining the construction of practical renormalisation schemes, also valid in the presence of composite operators. Furthermore, the formalism is used to derive various representations of modified symmetry relations in gauge theories, as well as to discuss gauge-invariant flows. We close with the construction and analysis of truncation schemes in view of practical optimisation.</description><identifier>ISSN: 0003-4916</identifier><identifier>EISSN: 1096-035X</identifier><identifier>DOI: 10.1016/j.aop.2007.01.007</identifier><identifier>CODEN: APNYA6</identifier><language>eng</language><publisher>New York: Elsevier Inc</publisher><subject>CORRELATION FUNCTIONS ; EQUATIONS OF MOTION ; Gauge field theories ; GAUGE INVARIANCE ; Mathematics ; OPTIMIZATION ; Physics ; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS ; QUANTUM FIELD THEORY ; Quantum theory ; Renormalisation ; Renormalisation group evolution of parameters ; Renormalisation group methods ; RENORMALIZATION ; SYMMETRY ; Theory</subject><ispartof>Annals of physics, 2007-12, Vol.322 (12), p.2831-2915</ispartof><rights>2007 Elsevier Inc.</rights><rights>Copyright © 2007 Elsevier B.V. All rights reserved.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c446t-a14ac5f14f5f33215f8e2fc5ea8ded9aa629b8a8c44245da74fe4987c4b94f153</citedby><cites>FETCH-LOGICAL-c446t-a14ac5f14f5f33215f8e2fc5ea8ded9aa629b8a8c44245da74fe4987c4b94f153</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0003491607000097$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>230,314,776,780,881,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/21077666$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Pawlowski, Jan M.</creatorcontrib><title>Aspects of the functional renormalisation group</title><title>Annals of physics</title><description>We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A simple equation for the flow of these relations is provided. The setting includes general flows in the presence of composite operators and their relation to standard flows, an important example being NPI quantities. We discuss optimisation and derive a functional optimisation criterion. Applications deal with the interrelation between functional flows and the quantum equations of motion, general Dyson–Schwinger equations. We discuss the combined use of these functional equations as well as outlining the construction of practical renormalisation schemes, also valid in the presence of composite operators. Furthermore, the formalism is used to derive various representations of modified symmetry relations in gauge theories, as well as to discuss gauge-invariant flows. We close with the construction and analysis of truncation schemes in view of practical optimisation.</description><subject>CORRELATION FUNCTIONS</subject><subject>EQUATIONS OF MOTION</subject><subject>Gauge field theories</subject><subject>GAUGE INVARIANCE</subject><subject>Mathematics</subject><subject>OPTIMIZATION</subject><subject>Physics</subject><subject>PHYSICS OF ELEMENTARY PARTICLES AND FIELDS</subject><subject>QUANTUM FIELD THEORY</subject><subject>Quantum theory</subject><subject>Renormalisation</subject><subject>Renormalisation group evolution of parameters</subject><subject>Renormalisation group methods</subject><subject>RENORMALIZATION</subject><subject>SYMMETRY</subject><subject>Theory</subject><issn>0003-4916</issn><issn>1096-035X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLxDAUhYMoOI7-AHdF1625eTXF1TD4ggE3Cu5CJk2clpmmJq3gvzelLgTB1YHLdy4fB6FLwAVgEDdtoX1fEIzLAkOR4ggtAFcix5S_HaMFxpjmrAJxis5ibDEGYFwu0M0q9tYMMfMuG3Y2c2NnhsZ3ep8F2_lw0Psm6umSvQc_9ufoxOl9tBc_uUSv93cv68d88_zwtF5tcsOYGHINTBvugDnuKCXAnbTEGW61rG1daS1ItZVaJpowXuuSOcsqWRq2rZgDTpfoev7r49CoaJrBmp3xXZdkFQFclkKIRF3NVB_8x2jjoFo_hiQfFaFcclmyX6_-QiBkSQmhtEoUzJQJPsZgnepDc9DhSwFW08SqVWliNU2sMKgUqXM7d2xa4rOxYRK1nbF1EybP2jf_tL8B5PyCIA</recordid><startdate>20071201</startdate><enddate>20071201</enddate><creator>Pawlowski, Jan M.</creator><general>Elsevier Inc</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>L7M</scope><scope>OTOTI</scope></search><sort><creationdate>20071201</creationdate><title>Aspects of the functional renormalisation group</title><author>Pawlowski, Jan M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c446t-a14ac5f14f5f33215f8e2fc5ea8ded9aa629b8a8c44245da74fe4987c4b94f153</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>CORRELATION FUNCTIONS</topic><topic>EQUATIONS OF MOTION</topic><topic>Gauge field theories</topic><topic>GAUGE INVARIANCE</topic><topic>Mathematics</topic><topic>OPTIMIZATION</topic><topic>Physics</topic><topic>PHYSICS OF ELEMENTARY PARTICLES AND FIELDS</topic><topic>QUANTUM FIELD THEORY</topic><topic>Quantum theory</topic><topic>Renormalisation</topic><topic>Renormalisation group evolution of parameters</topic><topic>Renormalisation group methods</topic><topic>RENORMALIZATION</topic><topic>SYMMETRY</topic><topic>Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Pawlowski, Jan M.</creatorcontrib><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>OSTI.GOV</collection><jtitle>Annals of physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Pawlowski, Jan M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Aspects of the functional renormalisation group</atitle><jtitle>Annals of physics</jtitle><date>2007-12-01</date><risdate>2007</risdate><volume>322</volume><issue>12</issue><spage>2831</spage><epage>2915</epage><pages>2831-2915</pages><issn>0003-4916</issn><eissn>1096-035X</eissn><coden>APNYA6</coden><abstract>We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A simple equation for the flow of these relations is provided. The setting includes general flows in the presence of composite operators and their relation to standard flows, an important example being NPI quantities. We discuss optimisation and derive a functional optimisation criterion. Applications deal with the interrelation between functional flows and the quantum equations of motion, general Dyson–Schwinger equations. We discuss the combined use of these functional equations as well as outlining the construction of practical renormalisation schemes, also valid in the presence of composite operators. Furthermore, the formalism is used to derive various representations of modified symmetry relations in gauge theories, as well as to discuss gauge-invariant flows. We close with the construction and analysis of truncation schemes in view of practical optimisation.</abstract><cop>New York</cop><pub>Elsevier Inc</pub><doi>10.1016/j.aop.2007.01.007</doi><tpages>85</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0003-4916 |
| ispartof | Annals of physics, 2007-12, Vol.322 (12), p.2831-2915 |
| issn | 0003-4916 1096-035X |
| language | eng |
| recordid | cdi_osti_scitechconnect_21077666 |
| source | ScienceDirect Journals (5 years ago - present) |
| subjects | CORRELATION FUNCTIONS EQUATIONS OF MOTION Gauge field theories GAUGE INVARIANCE Mathematics OPTIMIZATION Physics PHYSICS OF ELEMENTARY PARTICLES AND FIELDS QUANTUM FIELD THEORY Quantum theory Renormalisation Renormalisation group evolution of parameters Renormalisation group methods RENORMALIZATION SYMMETRY Theory |
| title | Aspects of the functional renormalisation group |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-30T22%3A18%3A21IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_osti_&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Aspects%20of%20the%20functional%20renormalisation%20group&rft.jtitle=Annals%20of%20physics&rft.au=Pawlowski,%20Jan%20M.&rft.date=2007-12-01&rft.volume=322&rft.issue=12&rft.spage=2831&rft.epage=2915&rft.pages=2831-2915&rft.issn=0003-4916&rft.eissn=1096-035X&rft.coden=APNYA6&rft_id=info:doi/10.1016/j.aop.2007.01.007&rft_dat=%3Cproquest_osti_%3E3711603161%3C/proquest_osti_%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1687322339&rft_id=info:pmid/&rft_els_id=S0003491607000097&rfr_iscdi=true |