Topological graph polynomials and quantum field theory part I: Heat kernel theories

Thomas Krajewski; Vincent Rivasseau; Adrian Tanasǎ; Zhituo Wang

doi:10.4171/JNCG/49

Topological graph polynomials and quantum field theory part I: Heat kernel theories

Thomas Krajewski^*
, Vincent Rivasseau
, Adrian Tanasǎ
, Zhituo Wang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

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 Bollobás-Riordan polynomials.

Original language	English
Pages (from-to)	29-82
Number of pages	54
Journal	Journal of Noncommutative Geometry
Volume	4
Issue number	1
DOIs	https://doi.org/10.4171/JNCG/49
State	Published - 2010
Externally published	Yes

Keywords

Bollobas-riordan polynomial
Parametric representation in (non)commutative field theory
Tutte polynomial

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Cite this

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abstract = "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 Bollob{\'a}s-Riordan polynomials.",

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author = "Thomas Krajewski and Vincent Rivasseau and Adrian Tanasǎ and Zhituo Wang",

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AU - Rivasseau, Vincent

AU - Tanasǎ, Adrian

AU - Wang, Zhituo

PY - 2010

Y1 - 2010

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AB - 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 Bollobás-Riordan polynomials.

KW - Bollobas-riordan polynomial

KW - Parametric representation in (non)commutative field theory

KW - Tutte polynomial

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U2 - 10.4171/JNCG/49

DO - 10.4171/JNCG/49

M3 - 文章

AN - SCOPUS:75349092688

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JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

IS - 1

ER -

Topological graph polynomials and quantum field theory part I: Heat kernel theories

Abstract

Keywords

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