Recursive Graph Invariants and Tropical Approximations in Quantum Field Theory

The Hepp bound is a graph invariant which arises as the tropical approximation of scalar quantum field theories. It provides a bound on Feynman integrals and encodes their leading divergences. The Hepp bound admits a combinatorial description as a recursion over edge deletions of the graph, and satisfies certain factorisation properties across graphs. I will define a broader class of generalised Hepp bounds that share the recursive structure of the Hepp bound, and present sufficient conditions for invariants in this class to share the aforementioned factorisation properties.