Generalization of the Bollobas-Riordan polynomial for tensor graphs

被引：9

作者：

Tanasa, Adrian ^{[1
,2
]}

机构：

[1] Univ Paris 13, CNRS, LIPN, Inst Galilee,UMR 7030, F-93430 Villetaneuse, France

[2] Inst Fiz Ingn Nucl Horia Hulubei, Dept Fiz Teoret, Magurele 077125, Romania

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2011年 / 52卷 / 07期

关键词：

GROUP FIELD-THEORY; PARAMETRIC REPRESENTATION; MODELS; INVARIANT; SURFACES; SCALAR;

D O I：

10.1063/1.3605312

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Tensor models are used nowadays for implementing a fundamental theory of quantum gravity. We define here a polynomial T encoding the supplementary topological information. This polynomial is a natural generalization of the Bollobas-Riordan polynomial (used to characterize matrix graphs) and is different from the Gurau polynomial [R. Gurau, Ann. Henri Poincare 11, 565 (2010)], defined for a particular class of tensor graphs, the colorable ones. The polynomial T is defined for both colorable and non-colorable graphs and it is proved to satisfy the deletion/contraction relation. A non-trivial example of a non-colorable graphs is analyzed. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3605312]

引用

页数：17