The Construction of Spin Foam Vertex Amplitudes
Spin foam vertex amplitudes are the key ingredient of spin foam models for quantum gravity. These fall into the realm of discretized path integral, and can be seen as generalized lattice gauge theories. They can be seen as an attempt at a 4-dimensional generalization of the Ponzano-Regge model for 3...
Збережено в:
| Дата: | 2013 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149216 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The Construction of Spin Foam Vertex Amplitudes / E. Bianchi, F. Hellmann // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 105 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149216 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1492162019-02-20T01:28:29Z The Construction of Spin Foam Vertex Amplitudes Bianchi, E. Hellmann, F. Spin foam vertex amplitudes are the key ingredient of spin foam models for quantum gravity. These fall into the realm of discretized path integral, and can be seen as generalized lattice gauge theories. They can be seen as an attempt at a 4-dimensional generalization of the Ponzano-Regge model for 3d quantum gravity. We motivate and review the construction of the vertex amplitudes of recent spin foam models, giving two different and complementary perspectives of this construction. The first proceeds by extracting geometric configurations from a topological theory of the BF type, and can be seen to be in the tradition of the work of Barrett, Crane, Freidel and Krasnov. The second keeps closer contact to the structure of Loop Quantum Gravity and tries to identify an appropriate set of constraints to define a Lorentz-invariant interaction of its quanta of space. This approach is in the tradition of the work of Smolin, Markopoulous, Engle, Pereira, Rovelli and Livine. 2013 Article The Construction of Spin Foam Vertex Amplitudes / E. Bianchi, F. Hellmann // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 105 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81T25; 81T45 DOI: http://dx.doi.org/10.3842/SIGMA.2013.008 http://dspace.nbuv.gov.ua/handle/123456789/149216 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Spin foam vertex amplitudes are the key ingredient of spin foam models for quantum gravity. These fall into the realm of discretized path integral, and can be seen as generalized lattice gauge theories. They can be seen as an attempt at a 4-dimensional generalization of the Ponzano-Regge model for 3d quantum gravity. We motivate and review the construction of the vertex amplitudes of recent spin foam models, giving two different and complementary perspectives of this construction. The first proceeds by extracting geometric configurations from a topological theory of the BF type, and can be seen to be in the tradition of the work of Barrett, Crane, Freidel and Krasnov. The second keeps closer contact to the structure of Loop Quantum Gravity and tries to identify an appropriate set of constraints to define a Lorentz-invariant interaction of its quanta of space. This approach is in the tradition of the work of Smolin, Markopoulous, Engle, Pereira, Rovelli and Livine. |
| format |
Article |
| author |
Bianchi, E. Hellmann, F. |
| spellingShingle |
Bianchi, E. Hellmann, F. The Construction of Spin Foam Vertex Amplitudes Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Bianchi, E. Hellmann, F. |
| author_sort |
Bianchi, E. |
| title |
The Construction of Spin Foam Vertex Amplitudes |
| title_short |
The Construction of Spin Foam Vertex Amplitudes |
| title_full |
The Construction of Spin Foam Vertex Amplitudes |
| title_fullStr |
The Construction of Spin Foam Vertex Amplitudes |
| title_full_unstemmed |
The Construction of Spin Foam Vertex Amplitudes |
| title_sort |
construction of spin foam vertex amplitudes |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149216 |
| citation_txt |
The Construction of Spin Foam Vertex Amplitudes / E. Bianchi, F. Hellmann // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 105 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT bianchie theconstructionofspinfoamvertexamplitudes AT hellmannf theconstructionofspinfoamvertexamplitudes AT bianchie constructionofspinfoamvertexamplitudes AT hellmannf constructionofspinfoamvertexamplitudes |
| first_indexed |
2023-05-20T17:32:15Z |
| last_indexed |
2023-05-20T17:32:15Z |
| _version_ |
1796153506014429184 |