Topological graph polynomials and quantum field theory Part I: heat kernel theories

被引：26

作者：

Krajewski, Thomas ^{[1
,2
]}

Rivasseau, Vincent ^{[3
]}

Tanasa, Adrian ^{[4
,5
]}

Wang, Zhituo ^{[4
]}

机构：

[1] Univ Paris 11, Phys Theor Lab, CNRS, UMR 8627, F-91405 Orsay, France

[2] CNRS, Ctr Phys Theor, Case 907, UMR 6207, F-13288 Marseille 9, France

[3] Univ Paris 11, Phys Theor Lab, CNRS, UMR 8627, F-91405 Orsay, France

[4] Ecole Polytech, Ctr Phys Theor, CNRS, UMR 7644, F-91128 Palaiseau, France

[5] Inst Fiz Ingn Nucl H Hulubei, Dep Fiz Teoret, Bucharest 077125, Romania

来源：

JOURNAL OF NONCOMMUTATIVE GEOMETRY | 2010年 / 4卷 / 01期

关键词：

Parametric representation in (non)commutative field theory; Tutte polynomial; Bollobas-Riordan polynomial; HOCHSCHILD CO-CHAINS; MODULI SPACE ACTIONS; BETA-FUNCTION; PARAMETRIC REPRESENTATION; RENORMALIZATION; INVARIANT; SCALAR; DUALITY; MOTIVES; MODELS;

D O I：

10.4171/JNCG/49

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the relationship between the universal topological polynomials for graphs in mathematics and the parametric representation of Feynman amplitudes in quantum field theory. In this first article we consider translation invariant theories with the usual heat-kernel-based propagator. We show how the Symanzik polynomials of quantum field theory are particular multivariate versions of the Tutte polynomial, and how the new polynomials of noncommutative quantum field theory are special versions of the Bollobas-Riordan polynomials.

引用

页码：29 / 82

页数：54

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