Entanglement entropy of a Maxwell field on the sphere
We compute the logarithmic coefficient of the entanglement entropy on asphere for a Maxwell field in <span class="MathJax_Preview">d=4</span> dimensions. In spherical coordinates theproblem decomposes into one dimensional ones along the radial coordinate foreach angular momentum. We show the entangl...
| Authors: | ; |
|---|---|
| Format: | Article |
| Status: | Published version |
| Publication date: | 2016 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/180622 |
| Online Access: | http://hdl.handle.net/11336/180622 |
| Access Level: | Open access |
| Keyword: | ENTROPY MAXWELL https://purl.org/becyt/ford/1.3 https://purl.org/becyt/ford/1 |
| _version_ | 1878403025478877184 |
|---|---|
| author | Casini, Horacio German |
| author2 | Huerta, Marina |
| author2_role | author |
| author_browse | Casini, Horacio German Huerta, Marina |
| author_facet | Casini, Horacio German Huerta, Marina |
| author_role | author |
| collection | CONICET Digital (CONICET) |
| description | We compute the logarithmic coefficient of the entanglement entropy on asphere for a Maxwell field in <span class="MathJax_Preview">d=4</span> dimensions. In spherical coordinates theproblem decomposes into one dimensional ones along the radial coordinate foreach angular momentum. We show the entanglement entropy of a Maxwell field isequivalent to the one of two identical massless scalars from which the mode of<span class="MathJax_Preview">l=0</span> has been removed. This shows the relation <span class="MathJax_Preview">c^M_{log}=2(c^S_{log}-c^{S_{l=0}}_{log})</span> between the logarithmic coefficient in theentropy for a Maxwell field <span class="MathJax_Preview">c^M_{log}</span>, the one for a <span class="MathJax_Preview">d=4</span> massless scalar<span class="MathJax_Preview">c_{log}^S</span>, and the logarithmic coefficient <span class="MathJax_Preview">c^{S_{l=0}}_{log}</span> for a <span class="MathJax_Preview">d=2</span>scalar with Dirichlet boundary condition at the origin. Using the acceptedvalues for these coefficients <span class="MathJax_Preview">c_{log}^S=-1/90</span> and <span class="MathJax_Preview">c^{S_{l=0}}_{log}=1/6</span>we get <span class="MathJax_Preview">c^M_{log}=-16/45</span>, which coincides with Dowker´s calculation, but doesnot match the coefficient <span class="MathJax_Preview">-rac{31}{45}</span> in the trace anomaly for a Maxwellfield. We have numerically evaluated these three numbers <span class="MathJax_Preview">c^M_{log}</span>,<span class="MathJax_Preview">c^S_{log}</span> and <span class="MathJax_Preview">c^{S_{l=0}}_{log}</span>, verifying the relation, as well aschecked they coincide with the corresponding logarithmic term in mutualinformation of two concentric spheres. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | AR_2efd9eaa4bd47e7b07082ee5d4e2147f |
| identifier_str_mv | Casini, Horacio German; Huerta, Marina; Entanglement entropy of a Maxwell field on the sphere; American Physical Society; Physical Review D: Particles, Fields, Gravitation and Cosmology; 93; 10; 1-2016; 1-18 1550-7998 CONICET Digital CONICET |
| institution | Consejo Nacional de Investigaciones Científicas y Técnicas |
| instname_str | Consejo Nacional de Investigaciones Científicas y Técnicas |
| language | eng |
| network_acronym_str | AR |
| network_name_str | Argentina |
| oai_identifier_str | oai:ri.conicet.gov.ar:11336/180622 |
| publishDate | 2016 |
| publishDateSort | 2016 |
| publisher | American Physical Society |
| publisherStr | American Physical Society |
| reponame_str | CONICET Digital (CONICET) |
| spelling | Entanglement entropy of a Maxwell field on the sphere Casini, Horacio German Huerta, Marina ENTROPY MAXWELL https://purl.org/becyt/ford/1.3 https://purl.org/becyt/ford/1 We compute the logarithmic coefficient of the entanglement entropy on asphere for a Maxwell field in <span class="MathJax_Preview">d=4</span> dimensions. In spherical coordinates theproblem decomposes into one dimensional ones along the radial coordinate foreach angular momentum. We show the entanglement entropy of a Maxwell field isequivalent to the one of two identical massless scalars from which the mode of<span class="MathJax_Preview">l=0</span> has been removed. This shows the relation <span class="MathJax_Preview">c^M_{log}=2(c^S_{log}-c^{S_{l=0}}_{log})</span> between the logarithmic coefficient in theentropy for a Maxwell field <span class="MathJax_Preview">c^M_{log}</span>, the one for a <span class="MathJax_Preview">d=4</span> massless scalar<span class="MathJax_Preview">c_{log}^S</span>, and the logarithmic coefficient <span class="MathJax_Preview">c^{S_{l=0}}_{log}</span> for a <span class="MathJax_Preview">d=2</span>scalar with Dirichlet boundary condition at the origin. Using the acceptedvalues for these coefficients <span class="MathJax_Preview">c_{log}^S=-1/90</span> and <span class="MathJax_Preview">c^{S_{l=0}}_{log}=1/6</span>we get <span class="MathJax_Preview">c^M_{log}=-16/45</span>, which coincides with Dowker´s calculation, but doesnot match the coefficient <span class="MathJax_Preview">-rac{31}{45}</span> in the trace anomaly for a Maxwellfield. We have numerically evaluated these three numbers <span class="MathJax_Preview">c^M_{log}</span>,<span class="MathJax_Preview">c^S_{log}</span> and <span class="MathJax_Preview">c^{S_{l=0}}_{log}</span>, verifying the relation, as well aschecked they coincide with the corresponding logarithmic term in mutualinformation of two concentric spheres. Fil: Casini, Horacio German. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina Fil: Huerta, Marina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina American Physical Society http://hdl.handle.net/11336/180622 Casini, Horacio German; Huerta, Marina; Entanglement entropy of a Maxwell field on the sphere; American Physical Society; Physical Review D: Particles, Fields, Gravitation and Cosmology; 93; 10; 1-2016; 1-18 1550-7998 CONICET Digital CONICET |
| spellingShingle | Entanglement entropy of a Maxwell field on the sphere Casini, Horacio German ENTROPY MAXWELL https://purl.org/becyt/ford/1.3 https://purl.org/becyt/ford/1 |
| status_str | publishedVersion |
| title | Entanglement entropy of a Maxwell field on the sphere |
| title_full | Entanglement entropy of a Maxwell field on the sphere |
| title_fullStr | Entanglement entropy of a Maxwell field on the sphere |
| title_full_unstemmed | Entanglement entropy of a Maxwell field on the sphere |
| title_short | Entanglement entropy of a Maxwell field on the sphere |
| title_sort | Entanglement entropy of a Maxwell field on the sphere |
| topic | ENTROPY MAXWELL https://purl.org/becyt/ford/1.3 https://purl.org/becyt/ford/1 |
| topic_facet | ENTROPY MAXWELL https://purl.org/becyt/ford/1.3 https://purl.org/becyt/ford/1 |
| url | http://hdl.handle.net/11336/180622 |