No Cover Image

Journal article 522 views 90 downloads

On the scalar curvature for the noncommutative four torus

Farzad Fathizadeh, Farzad Fathi Zadeh

Journal of Mathematical Physics, Volume: 56, Issue: 6, Start page: 062303

Swansea University Author: Farzad Fathi Zadeh

Check full text

DOI (Published version): 10.1063/1.4922815

Abstract

The canonical flat metric of the noncommutative four torus is conformally perturbed and the term corresponding to the scalar curvature in the heat kernel expansion of perturbed Laplacian is calculated by using an analog of the Wodziski residue. This allows the calculation to be done without using th...

Full description

Published in: Journal of Mathematical Physics
ISSN: 0022-2488 1089-7658
Published: 2015
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa40173
Tags: Add Tag
No Tags, Be the first to tag this record!
first_indexed 2018-05-15T19:27:45Z
last_indexed 2019-08-16T15:02:36Z
id cronfa40173
recordtype SURis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2019-08-16T10:50:27.8036527</datestamp><bib-version>v2</bib-version><id>40173</id><entry>2018-05-15</entry><title>On the scalar curvature for the noncommutative four torus</title><swanseaauthors><author><sid>c1859f5040a279bcd3fa991d8f6e7f21</sid><firstname>Farzad</firstname><surname>Fathi Zadeh</surname><name>Farzad Fathi Zadeh</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2018-05-15</date><deptcode>SCS</deptcode><abstract>The canonical flat metric of the noncommutative four torus is conformally perturbed and the term corresponding to the scalar curvature in the heat kernel expansion of perturbed Laplacian is calculated by using an analog of the Wodziski residue. This allows the calculation to be done without using the so called rearrangement lemma. Thus, because of the simplicity of the method, the structure of the one and two variable of functions of a modular automorphism that appear in the formula for the curvature can be understood and functional relations among them are discovered. Also the gradient of the analog of the Einstein-Hilbert action is calculated explicitly, which prepares the ground for defining certain geometric flows (such as the Yamabe flow) on the noncommutative four torus.</abstract><type>Journal Article</type><journal>Journal of Mathematical Physics</journal><volume>56</volume><journalNumber>6</journalNumber><paginationStart>062303</paginationStart><publisher/><issnPrint>0022-2488</issnPrint><issnElectronic>1089-7658</issnElectronic><keywords/><publishedDay>25</publishedDay><publishedMonth>6</publishedMonth><publishedYear>2015</publishedYear><publishedDate>2015-06-25</publishedDate><doi>10.1063/1.4922815</doi><url/><notes/><college>COLLEGE NANME</college><department>Computer Science</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>SCS</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2019-08-16T10:50:27.8036527</lastEdited><Created>2018-05-15T16:14:01.2025264</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Mathematics</level></path><authors><author><firstname>Farzad</firstname><surname>Fathizadeh</surname><order>1</order></author><author><firstname>Farzad</firstname><surname>Fathi Zadeh</surname><order>2</order></author></authors><documents><document><filename>0040173-16052018103937.pdf</filename><originalFilename>Nc4SC.pdf</originalFilename><uploaded>2018-05-16T10:39:37.9770000</uploaded><type>Output</type><contentLength>429014</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2018-05-16T00:00:00.0000000</embargoDate><copyrightCorrect>true</copyrightCorrect><language>eng</language></document></documents><OutputDurs/></rfc1807>
spelling 2019-08-16T10:50:27.8036527 v2 40173 2018-05-15 On the scalar curvature for the noncommutative four torus c1859f5040a279bcd3fa991d8f6e7f21 Farzad Fathi Zadeh Farzad Fathi Zadeh true false 2018-05-15 SCS The canonical flat metric of the noncommutative four torus is conformally perturbed and the term corresponding to the scalar curvature in the heat kernel expansion of perturbed Laplacian is calculated by using an analog of the Wodziski residue. This allows the calculation to be done without using the so called rearrangement lemma. Thus, because of the simplicity of the method, the structure of the one and two variable of functions of a modular automorphism that appear in the formula for the curvature can be understood and functional relations among them are discovered. Also the gradient of the analog of the Einstein-Hilbert action is calculated explicitly, which prepares the ground for defining certain geometric flows (such as the Yamabe flow) on the noncommutative four torus. Journal Article Journal of Mathematical Physics 56 6 062303 0022-2488 1089-7658 25 6 2015 2015-06-25 10.1063/1.4922815 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2019-08-16T10:50:27.8036527 2018-05-15T16:14:01.2025264 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Farzad Fathizadeh 1 Farzad Fathi Zadeh 2 0040173-16052018103937.pdf Nc4SC.pdf 2018-05-16T10:39:37.9770000 Output 429014 application/pdf Accepted Manuscript true 2018-05-16T00:00:00.0000000 true eng
title On the scalar curvature for the noncommutative four torus
spellingShingle On the scalar curvature for the noncommutative four torus
Farzad Fathi Zadeh
title_short On the scalar curvature for the noncommutative four torus
title_full On the scalar curvature for the noncommutative four torus
title_fullStr On the scalar curvature for the noncommutative four torus
title_full_unstemmed On the scalar curvature for the noncommutative four torus
title_sort On the scalar curvature for the noncommutative four torus
author_id_str_mv c1859f5040a279bcd3fa991d8f6e7f21
author_id_fullname_str_mv c1859f5040a279bcd3fa991d8f6e7f21_***_Farzad Fathi Zadeh
author Farzad Fathi Zadeh
author2 Farzad Fathizadeh
Farzad Fathi Zadeh
format Journal article
container_title Journal of Mathematical Physics
container_volume 56
container_issue 6
container_start_page 062303
publishDate 2015
institution Swansea University
issn 0022-2488
1089-7658
doi_str_mv 10.1063/1.4922815
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description The canonical flat metric of the noncommutative four torus is conformally perturbed and the term corresponding to the scalar curvature in the heat kernel expansion of perturbed Laplacian is calculated by using an analog of the Wodziski residue. This allows the calculation to be done without using the so called rearrangement lemma. Thus, because of the simplicity of the method, the structure of the one and two variable of functions of a modular automorphism that appear in the formula for the curvature can be understood and functional relations among them are discovered. Also the gradient of the analog of the Einstein-Hilbert action is calculated explicitly, which prepares the ground for defining certain geometric flows (such as the Yamabe flow) on the noncommutative four torus.
published_date 2015-06-25T03:51:08Z
_version_ 1763752509563731968
score 11.016481

Similar Items