an:01966593
Zbl 1033.81061
Connes, A.; Kreimer, D.
Insertion and elimination: The doubly infinite Lie algebra of Feynman graphs
EN
Ann. Henri Poincar?? 3, No. 3, 411-433 (2002).
00086228
2002
j
81T18 81T15 81T05 16W30 17B81 81Q30
quantum field theory; Hopf algebras; Feynman graphs
The aim is to algebraically describe the operations of elimination and insertion of subgraphs in the context of Feynman graphs. This is exhibited by identitfying such operations with representations of certain Hopf algebras and Lie algebra associated to Feynman graphs. The authors use their previous groundbreaking work regarding the Hopf algebras \({\mathcal H}_{\text{cm}}\) and \({\mathcal H}_{\text{rt}}\) introduced in [Commun. Math. Phys. 199, 203-242 (1998; Zbl 0932.16038)]. The insertions and eliminations do not commute, so the authors construct a larger Lie algebra which is studied in detail.
This work is important because the algebraic structures provided cover all operations in the perturbative expansion of a QFT.
Antun Milas (Tucson)
Zbl 0932.16038