Four-Dimensional Spin Foam Perturbation Theory
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Four-Dimensional Spin Foam Perturbation Theory
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| Creator |
Martins, J.F.
Mikovic, A. |
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| 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.
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| Date |
2019-02-14T17:48:13Z
2019-02-14T17:48:13Z 2011 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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