Scheme for building a t'Hooft-Polyakov monopole
We study a simple quantum mechanical model of a spinning particle moving on a sphere in the presence of a magnetic field. The system has two ground states. As the magnetic field is varied, the ground states mix through a non-Abelian Berry phase. We show that this Berry phase is the path ordered expo...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
American Physical Society
2011
|
| Online Access: | http://hdl.handle.net/1721.1/66697 |
| _version_ | 1826215923904675840 |
|---|---|
| author | Sonner, Julian Tong, David |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Sonner, Julian Tong, David |
| author_sort | Sonner, Julian |
| collection | MIT |
| description | We study a simple quantum mechanical model of a spinning particle moving on a sphere in the presence of a magnetic field. The system has two ground states. As the magnetic field is varied, the ground states mix through a non-Abelian Berry phase. We show that this Berry phase is the path ordered exponential of the smooth SU(2) ’t Hooft–Polyakov monopole. We further show that, by adjusting a potential on the sphere, the monopole becomes a Bogomol’nyi-Prasad-Sommerfield monopole and obeys the Bogomol’nyi equations. |
| first_indexed | 2024-09-23T16:39:11Z |
| format | Article |
| id | mit-1721.1/66697 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:39:11Z |
| publishDate | 2011 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/666972022-09-29T20:34:59Z Scheme for building a t'Hooft-Polyakov monopole Sonner, Julian Tong, David Massachusetts Institute of Technology. Center for Theoretical Physics Sonner, Julian Sonner, Julian We study a simple quantum mechanical model of a spinning particle moving on a sphere in the presence of a magnetic field. The system has two ground states. As the magnetic field is varied, the ground states mix through a non-Abelian Berry phase. We show that this Berry phase is the path ordered exponential of the smooth SU(2) ’t Hooft–Polyakov monopole. We further show that, by adjusting a potential on the sphere, the monopole becomes a Bogomol’nyi-Prasad-Sommerfield monopole and obeys the Bogomol’nyi equations. National Science Foundation (U.S.) (Grant No. PHY-0600465) United States. Dept. of Energy (cooperative research agreement No. DEFG02-05ER41360) Royal Society (Great Britain) 2011-11-01T13:36:34Z 2011-11-01T13:36:34Z 2009-05 2008-10 Article http://purl.org/eprint/type/JournalArticle 0031-9007 http://hdl.handle.net/1721.1/66697 Sonner, Julian, and David Tong. “Scheme for Building a ’t Hooft–Polyakov Monopole.” Physical Review Letters 102 (2009) © 2009 The American Physical Society. en_US http://dx.doi.org/10.1103/PhysRevLett.102.191801 Physical Review Letters Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Sonner, Julian Tong, David Scheme for building a t'Hooft-Polyakov monopole |
| title | Scheme for building a t'Hooft-Polyakov monopole |
| title_full | Scheme for building a t'Hooft-Polyakov monopole |
| title_fullStr | Scheme for building a t'Hooft-Polyakov monopole |
| title_full_unstemmed | Scheme for building a t'Hooft-Polyakov monopole |
| title_short | Scheme for building a t'Hooft-Polyakov monopole |
| title_sort | scheme for building a t hooft polyakov monopole |
| url | http://hdl.handle.net/1721.1/66697 |
| work_keys_str_mv | AT sonnerjulian schemeforbuildingathooftpolyakovmonopole AT tongdavid schemeforbuildingathooftpolyakovmonopole |