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A Combinatorial Perspective on Quantum Field TheoryWeight

A Combinatorial Perspective on Quantum Field Theory: Weight [In [1] Brown gave a technique for calculating Feynman periodsPeriod and Feynman integralsFeynman integral of certain graphsFeynman graph by step by step integration in parametric spaceParametric space. We will return to this algorithm in Chap. 16. For now, we will investigate a key part of the algorithm known as denominator reductionDenominator reduction. Denominator reduction is about keeping track of the denominators which show up over the course of the integration algorithm. These denominators are, like the Kirchhoff polynomialKirchhoff polynomial, polynomials which can be understood combinatorially. Furthermore they contain important information about the period as a whole. In particular they know about the weightWeighttranscendental which we will define in Sect. 14.2.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Combinatorial Perspective on Quantum Field TheoryWeight

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Publisher
Springer International Publishing
Copyright
© The Author(s) 2017
ISBN
978-3-319-47550-9
Pages
101 –107
DOI
10.1007/978-3-319-47551-6_14
Publisher site
See Chapter on Publisher Site

Abstract

[In [1] Brown gave a technique for calculating Feynman periodsPeriod and Feynman integralsFeynman integral of certain graphsFeynman graph by step by step integration in parametric spaceParametric space. We will return to this algorithm in Chap. 16. For now, we will investigate a key part of the algorithm known as denominator reductionDenominator reduction. Denominator reduction is about keeping track of the denominators which show up over the course of the integration algorithm. These denominators are, like the Kirchhoff polynomialKirchhoff polynomial, polynomials which can be understood combinatorially. Furthermore they contain important information about the period as a whole. In particular they know about the weightWeighttranscendental which we will define in Sect. 14.2.]

Published: Nov 26, 2016

Keywords: Integration Algorithm; Hodge Structure; Black Vertex; White Vertex; Weight Drop

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