Four-Dimensional Spin Foam Perturbation Theory
We define a four-dimensional spin-foam perturbation theory for the BF-theory with a B∧B potential term defined for a compact semi-simple Lie group G on a compact orientable 4-manifold M. This is done by using the formal spin foam perturbative series coming from the spin-foam generating functional. W...
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| Дата: | 2011 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147406 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Four-Dimensional Spin Foam Perturbation Theory / J.F. Martins, A. Mikovic // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 27 назв. — англ. |
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irk-123456789-1474062019-02-15T01:24:46Z Four-Dimensional Spin Foam Perturbation Theory Martins, J.F. Mikovic, A. We define a four-dimensional spin-foam perturbation theory for the BF-theory with a B∧B potential term defined for a compact semi-simple Lie group G on a compact orientable 4-manifold M. This is done by using the formal spin foam perturbative series coming from the spin-foam generating functional. We then regularize the terms in the perturbative series by passing to the category of representations of the quantum group Uq(g) where g is the Lie algebra of G and q is a root of unity. The Chain-Mail formalism can be used to calculate the perturbative terms when the vector space of intertwiners Λ⊗Λ→A, where A is the adjoint representation of g, is 1-dimensional for each irrep Λ. We calculate the partition function Z in the dilute-gas limit for a special class of triangulations of restricted local complexity, which we conjecture to exist on any 4-manifold M. We prove that the first-order perturbative contribution vanishes for finite triangulations, so that we define a dilute-gas limit by using the second-order contribution. We show that Z is an analytic continuation of the Crane-Yetter partition function. Furthermore, we relate Z to the partition function for the F∧F theory. 2011 Article Four-Dimensional Spin Foam Perturbation Theory / J.F. Martins, A. Mikovic // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 27 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81T25; 81T45; 57R56 DOI: http://dx.doi.org/10.3842/SIGMA.2011.094 http://dspace.nbuv.gov.ua/handle/123456789/147406 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 |
We define a four-dimensional spin-foam perturbation theory for the BF-theory with a B∧B potential term defined for a compact semi-simple Lie group G on a compact orientable 4-manifold M. This is done by using the formal spin foam perturbative series coming from the spin-foam generating functional. We then regularize the terms in the perturbative series by passing to the category of representations of the quantum group Uq(g) where g is the Lie algebra of G and q is a root of unity. The Chain-Mail formalism can be used to calculate the perturbative terms when the vector space of intertwiners Λ⊗Λ→A, where A is the adjoint representation of g, is 1-dimensional for each irrep Λ. We calculate the partition function Z in the dilute-gas limit for a special class of triangulations of restricted local complexity, which we conjecture to exist on any 4-manifold M. We prove that the first-order perturbative contribution vanishes for finite triangulations, so that we define a dilute-gas limit by using the second-order contribution. We show that Z is an analytic continuation of the Crane-Yetter partition function. Furthermore, we relate Z to the partition function for the F∧F theory. |
| format |
Article |
| author |
Martins, J.F. Mikovic, A. |
| spellingShingle |
Martins, J.F. Mikovic, A. Four-Dimensional Spin Foam Perturbation Theory Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Martins, J.F. Mikovic, A. |
| author_sort |
Martins, J.F. |
| title |
Four-Dimensional Spin Foam Perturbation Theory |
| title_short |
Four-Dimensional Spin Foam Perturbation Theory |
| title_full |
Four-Dimensional Spin Foam Perturbation Theory |
| title_fullStr |
Four-Dimensional Spin Foam Perturbation Theory |
| title_full_unstemmed |
Four-Dimensional Spin Foam Perturbation Theory |
| title_sort |
four-dimensional spin foam perturbation theory |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147406 |
| citation_txt |
Four-Dimensional Spin Foam Perturbation Theory / J.F. Martins, A. Mikovic // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 27 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT martinsjf fourdimensionalspinfoamperturbationtheory AT mikovica fourdimensionalspinfoamperturbationtheory |
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2023-05-20T17:27:38Z |
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2023-05-20T17:27:38Z |
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1796153349148508160 |