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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
Four-Dimensional Spin Foam Perturbation Theory
João Faria Martinsa, Aleksandar Mikovićbc a Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Quinta da Torre, 2829-516 Caparica, Portugal
b Departamento de Matemática, Universidade Lusófona de Humanidades e Tecnologia, Av do Campo Grande, 376, 1749-024 Lisboa, Portugal
c Grupo de Física Matemática da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal
Аннотация:
We define a four-dimensional spin-foam perturbation theory for the ${\rm BF}$-theory with a $B\wedge B$ 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 $U_q (\mathfrak{g})$ where $\mathfrak{g}$ 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 $\Lambda\otimes \Lambda \to A$, where $A$ is the adjoint representation of $\mathfrak{g}$, is 1-dimensional for each irrep $\Lambda$. 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 $F\wedge F$ theory.
Ключевые слова:
spin foam models; BF-theory; spin networks; dilute-gas limit; Crane–Yetter invariant; spin-foam perturbation theory.
Поступила: 3 июня 2011 г.; в окончательном варианте 23 сентября 2011 г.; опубликована 11 октября 2011 г.
Образец цитирования:
João Faria Martins, Aleksandar Miković, “Four-Dimensional Spin Foam Perturbation Theory”, SIGMA, 7 (2011), 094, 22 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma652 https://www.mathnet.ru/rus/sigma/v7/p94
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