Insertion and elimination Lie algebra: The ladder case

Letters in Mathematical Physics

Volumn 67, Issue 1, 2004, Pages 61-74

  Mencattini, Igor ^a   Kreimer, Dirk ^b  

^a Boston University   (United States)

^b CNRS   (France)

Author keywords

Dyson Schwinger equations; Feynman graphs; Heisenberg algebra; Insertion elimination Lie algebras; Ladder graphs

Indexed keywords

EID: 3943081339     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:MATH.0000027749.09118.a5     Document Type: Article

References (8)

1. Broadhurst, D. J. and Kreimer, D.: Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality, Nuclear Phys. B 600 (2001), 403 [arXiv:hep-th/0012146].
2. Connes, A. and Kreimer, D.: Renormalization in quantum field theory and the Riemann Hilbert problem. I. The Hopf algebra structure of graphs and the main theorem, Comm. Math. Phys. 210(1) (2000), 249-273.
3. Connes, A. and Kreimer, D.: Renormalization in quantum field theory and the Riemann Hilbert problem. II. The β-function, diffeomorphism and the renormalization group, Comm. Math. Phys. 216(1) (2001), 215-241.
4. Connes, A. and Kreimer, D.: Insertion and Elimination: the doubly infinite Lie algebra of Feynmann graphs, Ann. Henri Poincare 3(3) (2002), 411-433.
5. Kac V.: Infinite Dimensional Lie Algebras, 2nd edn, Cambridge University Press, 1994.
6. Kac, V. and Raina, A.: Bombay Lectures on Highest Weight Representation of Infinite Dimensional Lie Algebras, Adv. Ser. Math. Phys. 2, World Scientific, Singapore, 1988.
7. Kreimer, D.: On the Hopf algebra structure of perturbative quantum field theory, Adv. Theor. Math. Phys. 2(2) (1998).
8. Milnor, J. W. and Moore, J. C.: On the Structure of Hopf Algebras, Ann. of Math. 81(2) (1965), 211-264.