Algebraic lattices in QFT renormalization

Understand

The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory.

• It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices.
• This class of QFTs includes the Standard model.
• In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular.