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dc.contributor.author Martins, J.F.
dc.contributor.author Mikovic, A.
dc.date.accessioned 2019-02-14T17:48:13Z
dc.date.available 2019-02-14T17:48:13Z
dc.date.issued 2011
dc.identifier.citation 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. uk_UA
dc.identifier.issn 1815-0659
dc.identifier.other 2010 Mathematics Subject Classification: 81T25; 81T45; 57R56
dc.identifier.other DOI: http://dx.doi.org/10.3842/SIGMA.2011.094
dc.identifier.uri http://dspace.nbuv.gov.ua/handle/123456789/147406
dc.description.abstract 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. uk_UA
dc.description.sponsorship This work was partially supported FCT (Portugal) under the projects PTDC/MAT/099880/2008, PTDC/MAT/098770/2008, PTDC/MAT/101503/2008. This work was also partially supported by CMA/FCT/UNL, through the project PEst OE/MAT/UI0297/2011. uk_UA
dc.language.iso en uk_UA
dc.publisher Інститут математики НАН України uk_UA
dc.relation.ispartof Symmetry, Integrability and Geometry: Methods and Applications
dc.title Four-Dimensional Spin Foam Perturbation Theory uk_UA
dc.type Article uk_UA
dc.status published earlier uk_UA

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