Feynman diagrams and rooted maps

An optimal algorithm to generate rooted trivalent diagrams and rooted triangular maps

A trivalent diagram is a connected, two-colored bipartite graph (parallel edges allowed but not loops) such that every black vertex is of degree 1 or 3 and every white vertex is of degree 1 or 2, with a cyclic order imposed on every set of edges incident to to a same vertex. A rooted trivalent diagram is a trivalent diagram with a distinguished edge, its root. We shall describe and analyze an a...

Rooted Trees, Feynman Graphs, and Hecke Correspondences

We construct natural representations of the Connes-Kreimer Lie algebras on rooted trees/Feynman graphs arising from Hecke correspondences in the categories LRF ,LFG constructed by K. Kremnizer and the author. We thus obtain the insertion/elimination representations constructed by Connes-Kreimer as well as an isomorphic pair we term top-insertion/top-elimination. We also construct graded finite-...

Feynman diagrams versus Fermi-gas Feynman emulator

Grope Cobordism and Feynman Diagrams

We explain how the usual algebras of Feynman diagrams behave under the grope degree introduced in [CT]. We show that the Kontsevich integral rationally classifies grope cobordisms of knots in 3-space when the “class” is used to organize gropes. This implies that the grope cobordism equivalence relations are highly nontrivial in dimension 3. We also show that the class is not a useful organizing...

Matrix Theory and Feynman Diagrams

We briefly review the computation of graviton and antisymmetric tensor scattering amplitudes in Matrix Theory from a diagramatic S-Matrix point of view. It is by now commonly believed that eleven dimensional supergravity is the low-energy effective theory of a more fundamental microscopic model, known as M-theory. A proposed definition of M-theory has been given in terms of the large N limit of...