Topological Graph Polynomial and Quantum Field Theory Part II: Mehler Kernel Theories

We define a new topological polynomial extending the Bollobás–Riordan one, which obeys a four-term reduction relation of the deletion/contraction type and has a natural behaviour under partial duality. This allows to write down a completely explicit combinatorial evaluation of the polynomials, occur...

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Veröffentlicht in:Annales Henri Poincaré Jg. 12; H. 3; S. 483 - 545
Hauptverfasser: Krajewski, Thomas, Rivasseau, Vincent, Vignes-Tourneret, Fabien
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel SP Birkhäuser Verlag Basel 01.04.2011
Springer
Schlagworte:
Algebra
Classical and Quantum Gravitation
Combinatorics
Combinatorics. Ordered structures
Dynamical Systems and Ergodic Theory
Elementary Particles
Exact sciences and technology
Field theory and polynomials
Graph theory
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Other topics in mathematical methods in physics
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Relativity Theory
Sciences and techniques of general use
Theoretical
Ribbon Graph
Span Subgraph
Parametric Representation
Heat Kernel
Unicyclic Graph
Evaluation
Field theories
Topological graph
Duality
Graph theory
Contraction
Kernel method
Kernels
Deletion
Representation theory
Polynomials
Quantum field theory
Mathematical physics
ISSN:1424-0637, 1424-0661
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:We define a new topological polynomial extending the Bollobás–Riordan one, which obeys a four-term reduction relation of the deletion/contraction type and has a natural behaviour under partial duality. This allows to write down a completely explicit combinatorial evaluation of the polynomials, occurring in the parametric representation of the non-commutative Grosse–Wulkenhaar quantum field theory. An explicit solution of the parametric representation for commutative field theories based on the Mehler kernel is also provided.
ISSN:1424-0637
1424-0661
DOI:10.1007/s00023-011-0087-2