Decorated Feynman categories

Feynman diagrams versus Fermi-gas Feynman emulator

Decorated hypertrees

C. Jensen, J. McCammond and J. Meier have used weighted hypertrees to compute the Euler characteristic of a subgroup of the automorphism group of a free product. Weighted hypertrees also appear in the study of the homology of the hypertree poset. We link them to decorated hypertrees after a general study on decorated hypertrees, which we enumerate using box trees.

Decorated hypertrees

C. Jensen, J. McCammond and J. Meier have used weighted hypertrees to compute the Euler characteristic of a subgroup of the automorphism group of a free product. Weighted hypertrees also appear in the study of the homology of the hypertree poset. We link them to decorated hypertrees after a general study on decorated hypertrees, which we enumerate using box trees.

Decorated Corelations

Let C be a category with finite colimits, and let (E ,M) be a factorisation system on C with M stable under pushouts. Writing C;M for the symmetric monoidal category with morphisms cospans of the form c → m ←, where c ∈ C and m ∈ M, we give method for constructing a category from a symmetric lax monoidal functor F : (C;M,+) → (Set,×). A morphism in this category, termed a decorated corelation, ...

Supermanifolds from Feynman graphs

We generalize the computation of Feynman integrals of log divergent graphs in terms of the Kirchhoff polynomial to the case of graphs with both fermionic and bosonic edges, to which we assign a set of ordinary and Grassmann variables. This procedure gives a computation of the Feynman integrals in terms of a period on a supermanifold, for graphs admitting a basis of the first homology satisfying...