Combinatorics of (perturbative) quantum field theory

Physics Report

Volumn 363, Issue 4-6, 2002, Pages 387-424

  Kreimer, D ^a,b  

^a BOSTON UNIVERSITY   (United States)

^b INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036239309     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0370-1573(01)00099-0     Document Type: Review

References (72)

1. On the Hopf algebra structure of perturbative quantum field theories
2. Chen's iterated integral represents the operator product expansion
3. On overlapping divergences
4. Hopf algebras, renormalization and noncommutative geometry
5. Lessons from quantum field theory: Hopf algebras and spacetime geometries
6. Renormalization in quantum field theory and the Riemann-Hilbert problem
7. Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
8. Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The beta-function, diffeomorphisms and the renormalization group
9. Renormalization automated by Hopf algebra
10. Combination explosion of renormalization tamed by Hopf algebra: 30-loop Pade-Borel restummation
11. Towards cohomology of renormalization: Bigarding the combinatorial Hopf algebra of rooted trees
12. Shuffling quantum field theory
13. Feynman diagrams and polylogarithms: Shuffles and pentagons
14. Knots and Feynman Diagrams
15. Using the Hopf algebra structure of QFT in calculations
16. The role of locality in perturbation theory
17. Renormalized perturbation theory: A theoretical laboratory, talk given at Mathematical Physics in Mathematics and Physics
18. A compactification of configuration spaces
19. On Kreimer's Hopf algebra structure of Feynman graphs
20. Microlocal analysis and interacting quantum field theories: Renormalization on physical backgrounds
21. Über die Rolle von Hopfkategorien in störungstheoretischer Quantenfeldtheorie
22. La renaissance des opérades (The rebirth of operads) Séminaire Bourbaki
23. On the trees of quantum fields
24. Renormalization of QED with planary binary trees
25. Pre-Lie algebras and the rooted trees operad
26. The Riemann-Hilbert Problem
27. The structure of the invariant charge in massive theories with one coupling
28. Asymptotic normalization properties and mass independent renormalization group functions
29. Hopf algebras, cyclic cohomology and the transverse index theorem
30. Wave function renormalization and the Hopf algebra of Connes and Kreimer
31. Knots and numbers in Phi**4 theory to 7 loops and beyond
32. Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
33. 1 - 0.∞ and N-th root of unity)
34. Multiple Zeta Values, Galois groups, and geometry of modular varieties
35. The double logarithm and Manin's complex for modular curves
36. Multiple polylogarithms, cyclotomy and modular complexes
37. Evaluation of k-fold Euler-Zagier sums: A compendium of results for arbitrary k
38. Conjectured Enumeration of irreducible Multiple Zeta Values, from Knots and Feynman Diagrams
39. On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory
40. Values of Zeta-functions and their applications
41. Quasi Shuffle Products
42. On Associators and the Grothendieck Teichmüller Group I
43. On knots in subdivergent diagrams
44. On the invariance of residues of Feynman graphs
45. A short survey of noncommutative geometry
46. Unknotting the polarized vacuum of quenched QED
47. 5
48. 5
49. Renormalization and effective Lagrangians
50. Exact renormalization group equations: An introductory review
51. Runge-Kutta methods and renormalization
52. Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality
53. Asymptotic improvement of resummations and perturbative predictions in quantum field theory
54. An automized algorithm to compute infrared divergent multi-loop integrals
55. Problems of the strategy of regions
56. An algebraic approach to coarse graining
57. 4 in three dimensions Hamiltonian
58. Scaling algebras and renormalization group in algebraic quantum field theory
59. Algebraic QFT, perturbation theory and the loop expansion
60. Bogoliubov's recursion and integrability of effective actions
61. On renormalization group in abstract QFT
62. Convergence theorem for noncommutative Feynman graphs and renormalization
63. On the Connes-Kreimer construction of Hopf algebras
64. Relating the Connes-Kreimer and Grossman-Larson Hopf algebras built on rooted trees
65. Finite dimensional comodules over the Hopf algebras of rooted trees