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Volumn 38, Issue 50, 2005, Pages

The Hopf algebra approach to Feynman diagram calculations

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EID: 28844481081     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/38/50/R01     Document Type: Review
Times cited : (44)

References (119)
  • 2
    • 0040519930 scopus 로고    scopus 로고
    • Prepoisson algebras
    • Aguiar M 2000 Prepoisson algebras Lett. Math. Phys. 54 263-77
    • (2000) Lett. Math. Phys. , vol.54 , Issue.4 , pp. 263-277
    • Aguiar, M.1
  • 4
    • 84859322036 scopus 로고    scopus 로고
    • Structure of the Loday-Ronco Hopf algebra of trees
    • Aguiar M and Sottile F 2004 Structure of the Loday-Ronco Hopf algebra of trees J. Alg. to appear (Preprint math.CO/0409022)
    • (2004) J. Alg.
    • Aguiar, M.1    Sottile, F.2
  • 7
    • 0042725085 scopus 로고
    • Some aspects of Baxter's functional equation
    • Atkinson F V 1963 Some aspects of Baxter's functional equation J. Math. Anal. Appl. 7 1-30
    • (1963) J. Math. Anal. Appl. , vol.7 , Issue.1 , pp. 1-30
    • Atkinson, F.V.1
  • 9
    • 84972511438 scopus 로고
    • An analytic problem whose solution follows from a simple algebraic identity
    • Baxter G 1960 An analytic problem whose solution follows from a simple algebraic identity Pacific J. Math. 10 731-42
    • (1960) Pacific J. Math. , vol.10 , pp. 731-742
    • Baxter, G.1
  • 10
    • 18244405039 scopus 로고    scopus 로고
    • The Hopf algebra of rooted trees in Epstein-Glaser renormalization
    • Bergbauer C and Kreimer D 2005 The Hopf algebra of rooted trees in Epstein-Glaser renormalization Ann. Inst. Henri Poincaré 6 343-67 (Preprint hep-th/0403207)
    • (2005) Ann. Inst. Henri Poincaré , vol.6 , Issue.2 , pp. 343-367
    • Bergbauer, C.1    Kreimer, D.2
  • 12
    • 36149022296 scopus 로고
    • The electromagnetic shift of energy levels
    • Bethe H 1947 The electromagnetic shift of energy levels Phys. Rev. 72 339-41
    • (1947) Phys. Rev. , vol.72 , Issue.4 , pp. 339-341
    • Bethe, H.1
  • 13
    • 0035981685 scopus 로고    scopus 로고
    • On the invariance of residues of Feynman graphs
    • Bierenbaum I, Kreckel R and Kreimer D 2002 On the invariance of residues of Feynman graphs J. Math Phys. 43 4721-40 (Preprint hep-th/0111192)
    • (2002) J. Math Phys. , vol.43 , Issue.10 , pp. 4721-4740
    • Bierenbaum, I.1    Kreckel, R.2    Kreimer, D.3
  • 14
    • 2442505725 scopus 로고    scopus 로고
    • The massless two-loop two-point function
    • Bierenbaum I and Weinzierl S 2003 The massless two-loop two-point function Eur. Phys. J. C 32 67-78 (Preprint hep-ph/0308311)
    • (2003) Eur. Phys. J. , vol.32 , Issue.1 , pp. 67-78
    • Bierenbaum, I.1    Weinzierl, S.2
  • 15
    • 0009185954 scopus 로고
    • Field theory renormalization using Callan-Symanzik equation
    • Blaer A S and Young K 1974 Field theory renormalization using Callan-Symanzik equation Nucl. Phys. B 83 493-514
    • (1974) Nucl. Phys. , vol.83 , Issue.3 , pp. 493-514
    • Blaer, A.S.1    Young, K.2
  • 17
    • 0000813416 scopus 로고
    • On the multiplication of causal functions in the quantum theory of fields
    • Bogoluibov N N and Parasiuk O S 1957 On the multiplication of causal functions in the quantum theory of fields Acta Math. 97 227-66
    • (1957) Acta Math. , vol.97 , pp. 227-266
    • Bogoluibov, N.N.1    Parasiuk, O.S.2
  • 19
    • 28844505866 scopus 로고    scopus 로고
    • Hopf algebra of Feynman diagrams, renormalization and Wiener-Hopf factorization (following A Connes and D Kreimer)
    • de Monvel L Boutet 2003 Hopf algebra of Feynman diagrams, renormalization and Wiener-Hopf factorization (following A Connes and D Kreimer) Séminaire Bourbaki vol 2001/2002 pp 149-65 (Astérisque No. 290, Exp. No. 900, viii) (Paris: Société Mathématique de France)
    • (2003) Séminaire Bourbaki , vol.2001-2002 , pp. 149-165
    • De Monvel, L.B.1
  • 20
    • 0001330424 scopus 로고    scopus 로고
    • Renormalization automated by Hopf algebra
    • Broadhurst D J and Kreimer D 1999 Renormalization automated by Hopf algebra J. Symb. Comput. 27 581-600 (Preprint hep-th/9810087)
    • (1999) J. Symb. Comput. , vol.27 , Issue.6 , pp. 581-600
    • Broadhurst, D.J.1    Kreimer, D.2
  • 21
    • 0034708002 scopus 로고    scopus 로고
    • Combinatoric explosion of renormalization tamed by Hopf algebra: 30-loop pade-borel resummation
    • Broadhurst D J and Kreimer D 2000 Combinatoric explosion of renormalization tamed by Hopf algebra: 30-loop pade-borel resummation Phys. Lett. B 475 63-70 (Preprint hep-th/9912093)
    • (2000) Phys. Lett. , vol.475 , Issue.1-2 , pp. 63-70
    • Broadhurst, D.J.1    Kreimer, D.2
  • 22
    • 0002912762 scopus 로고    scopus 로고
    • Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality
    • Broadhurst D J and Kreimer D 2001 Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality Nucl. Phys. B 600 403-22 (Preprint hep-th/0012146)
    • (2001) Nucl. Phys. , vol.600 , Issue.2 , pp. 403-422
    • Broadhurst, D.J.1    Kreimer, D.2
  • 23
    • 0034336368 scopus 로고    scopus 로고
    • Towards cohomology of renormalization: Bigrading the combinatorial Hopf algebra of rooted trees
    • Broadhurst D J and Kreimer D 2000 Towards cohomology of renormalization: bigrading the combinatorial Hopf algebra of rooted trees Commun. Math. Phys. 215 217-36 (Preprint hep-th/0001202)
    • (2000) Commun. Math. Phys. , vol.215 , Issue.1 , pp. 217-236
    • Broadhurst, D.J.1    Kreimer, D.2
  • 24
    • 0347486047 scopus 로고    scopus 로고
    • Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops
    • Broadhurst D J and Kreimer D 1998 Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops Phys. Lett. B 426 339-46
    • (1998) Phys. Lett. , vol.426 , Issue.3-4 , pp. 339-346
    • Broadhurst, D.J.1    Kreimer, D.2
  • 25
    • 0039179700 scopus 로고    scopus 로고
    • Runge-Kutta methods and renormalization
    • Brouder Ch 2000 Runge-Kutta methods and renormalization Eur. Phys. J. C 12 512-34 (Preprint hep-th/9904014)
    • (2000) Eur. Phys. J. , vol.12 , Issue.3 , pp. 521-534
    • Ch, B.1
  • 27
    • 84968481790 scopus 로고
    • An algebraic theory of integration methods
    • Butcher J C 1972 An algebraic theory of integration methods Math. Comput. 26 117-
    • (1972) Math. Comput. , vol.26
    • Butcher, J.C.1
  • 28
    • 0001736474 scopus 로고
    • A simple approach to renormalization theory
    • Caswell W E and Kennedy A D 1982 A simple approach to renormalization theory Phys. Rev. D 25 392-408
    • (1982) Phys. Rev. , vol.25 , Issue.2 , pp. 392-408
    • Caswell, W.E.1    Kennedy, A.D.2
  • 29
    • 0000861949 scopus 로고
    • On the structure of free Baxter algebras
    • Cartier P 1972 On the structure of free Baxter algebras Adv. Math. 9 253-65
    • (1972) Adv. Math. , vol.9 , Issue.2 , pp. 253-265
    • Cartier, P.1
  • 30
    • 0008120736 scopus 로고    scopus 로고
    • Pre-Lie algebras and the rooted trees operad
    • Chapoton F and Livernet M 2001 Pre-Lie algebras and the rooted trees operad Int. Math. Res. Not. 395-408
    • (2001) Int. Math. Res. Not. , pp. 395-408
    • Chapoton, F.1    Livernet, M.2
  • 31
    • 0036108730 scopus 로고    scopus 로고
    • Normal coordinates and primitive elements in the Hopf algebra of renormalization
    • Chryssomalakos C, Quevedo H, Rosenbaum M and Vergara J D 2002 Normal coordinates and primitive elements in the Hopf algebra of renormalization Commun. Math. Phys. 225 465-85 (Preprint hep-th/0105252)
    • (2002) Commun. Math. Phys. , vol.225 , Issue.3 , pp. 465-485
    • Chryssomalakos, C.1    Quevedo, H.2    Rosenbaum, M.3    Vergara, J.D.4
  • 32
    • 0003787842 scopus 로고
    • Collins J C 1984 Renormalization (Cambridge Monographs on Mathematical Physics) (Cambridge: Cambridge University Press)
    • (1984) Renormalization
    • Collins, J.C.1
  • 33
    • 0032257297 scopus 로고    scopus 로고
    • Hopf algebras, renormalization and noncommutative geometry
    • Connes A and Kreimer D 1998 Hopf algebras, renormalization and noncommutative geometry Commun. Math. Phys. 199 203-42 (Preprint hep-th/9808042)
    • (1998) Commun. Math. Phys. , vol.199 , Issue.1 , pp. 203-242
    • Connes, A.1    Kreimer, D.2
  • 34
    • 0034349865 scopus 로고    scopus 로고
    • Renormalization in quantum field theory and the Riemann-Hilbert problem. I. The Hopf algebra structure of graphs and the main theorem
    • Connes A and Kreimer D 2000 Renormalization in quantum field theory and the Riemann-Hilbert problem. I. The Hopf algebra structure of graphs and the main theorem Commun. Math. Phys. 210 249-73 (Preprint hep-th/9912092)
    • (2000) Commun. Math. Phys. , vol.210 , Issue.1 , pp. 249-273
    • Connes, A.1    Kreimer, D.2
  • 35
    • 0035530562 scopus 로고    scopus 로고
    • Renormalization in quantum field theory and the Riemann-Hilbert problem. II. The β-function, diffeomorphisms and the renormalization group
    • Connes A and Kreimer D 2001 Renormalization in quantum field theory and the Riemann-Hilbert problem. II. The β-function, diffeomorphisms and the renormalization group Commun. Math. Phys. 216 215-41 (Preprint hep-th/0003188)
    • (2001) Commun. Math. Phys. , vol.216 , Issue.1 , pp. 215-241
    • Connes, A.1    Kreimer, D.2
  • 36
    • 0036436361 scopus 로고    scopus 로고
    • Insertion and elimination: The doubly infinite Lie algebra of Feynman graphs
    • Connes A and Kreimer D 2002 Insertion and elimination: the doubly infinite Lie algebra of Feynman graphs Ann. Inst. Henri Poincaré 3 411-33 (Preprint hep-th/0201157)
    • (2002) Ann. Inst. Henri Poincaré , vol.3 , Issue.3 , pp. 411-433
    • Connes, A.1    Kreimer, D.2
  • 38
    • 13244268440 scopus 로고    scopus 로고
    • Renormalization and Motivic Galois theory
    • Connes A and Marcolli M 2004 Renormalization and Motivic Galois theory Int. Math. Res. Not. 76 4073-91 (Preprint math.NT/0409306)
    • (2004) Int. Math. Res. Not. , vol.2004 , Issue.76 , pp. 4073-4091
    • Connes, A.1    Marcolli, M.2
  • 39
    • 25444459949 scopus 로고    scopus 로고
    • Quantum fields and moties
    • Connes A and Marcolli M 2006 Quantum fields and moties J. Geom. Phys. 56 55-85 (Preprint hep-th/0504085)
    • (2006) J. Geom. Phys. , vol.56 , Issue.1 , pp. 55-85
    • Connes, A.1    Marcolli, M.2
  • 40
    • 1042279725 scopus 로고    scopus 로고
    • A hint of renormalization
    • Delamotte B 2004 A hint of renormalization Am. J. Phys. 72 170-84 (Preprint hep-th/0212049)
    • (2004) Am. J. Phys. , vol.72 , Issue.2 , pp. 170-184
    • Delamotte, B.1
  • 41
    • 36149021943 scopus 로고
    • The S matrix in quantum electrodynamics
    • Dyson F 1949 The S matrix in quantum electrodynamics Phys. Rev. 75 1736-55
    • (1949) Phys. Rev. , vol.75 , Issue.11 , pp. 1736-1755
    • Dyson, F.1
  • 42
    • 0000563622 scopus 로고
    • The radiation theories of Tomonaga, Schwinger, and Feynman
    • Dyson F 1949 The radiation theories of Tomonaga, Schwinger, and Feynman Phys. Rev. 75 486-502
    • (1949) Phys. Rev. , vol.75 , Issue.3 , pp. 486-502
    • Dyson, F.1
  • 43
    • 0041314056 scopus 로고    scopus 로고
    • Loday-type algebras and the Rota-Baxter relation
    • Ebrahimi-Fard K 2002 Loday-type algebras and the Rota-Baxter relation Lett. Math. Phys. 61 139-47
    • (2002) Lett. Math. Phys. , vol.61 , Issue.2 , pp. 139-147
    • Ebrahimi-Fard, K.1
  • 44
    • 18244401353 scopus 로고    scopus 로고
    • Integrable renormalization II: The general case
    • Ebrahimi-Fard K, Guo L and Kreimer D 2005 Integrable renormalization II: the general case Ann. Inst. Henri Poincaré 6 369-95 (Preprint hep-th/0403118)
    • (2005) Ann. Inst. Henri Poincaré , vol.6 , Issue.2 , pp. 369-395
    • Ebrahimi-Fard, K.1    Guo, L.2    Kreimer, D.3
  • 45
    • 9944236213 scopus 로고    scopus 로고
    • Spiter's identity and the algebraic Birkhoff decomposition in pQFT
    • Ebrahimi-Fard K, Guo L and Kreimer D 2004 Spiter's identity and the algebraic Birkhoff decomposition in pQFT J. Phys. A: Math. Gen. 37 11037-52 (Preprint hep-th/0407082)
    • (2004) J. Phys. A: Math. Gen. , vol.37 , Issue.45 , pp. 11037-11052
    • Ebrahimi-Fard, K.1    Guo, L.2    Kreimer, D.3
  • 46
    • 28844497135 scopus 로고    scopus 로고
    • Mixable shuffles, quasi-shuffles and Hopf algebras
    • Ebrahimi-Fard K and Guo L 2005 Mixable shuffles, quasi-shuffles and Hopf algebras J. Alg. Comb. (Preprint hep-th/0506418)
    • (2005) J. Alg. Comb.
    • Ebrahimi-Fard, K.1    Guo, L.2
  • 50
    • 0030584844 scopus 로고    scopus 로고
    • On posets and Hopf algebras
    • Ehrenborg R 1996 On posets and Hopf algebras Adv. Math. 119 1-25
    • (1996) Adv. Math. , vol.119 , Issue.1 , pp. 1-25
    • Ehrenborg, R.1
  • 51
    • 0000515565 scopus 로고
    • The role of locality in perturbation theory
    • Epstein H and Glaser V 1973 The role of locality in perturbation theory Ann. Inst. Henri Poincaré A 19 211-95
    • (1973) Ann. Inst. Henri Poincaré , vol.19 , pp. 211-295
    • Epstein, H.1    Glaser, V.2
  • 53
    • 0035920317 scopus 로고    scopus 로고
    • On the antipode of Kreimer's Hopf algebra
    • Figueroa H and Gracia-Bondía J M 2001 On the antipode of Kreimer's Hopf algebra Mod. Phys. Lett. A 16 1427-34 (Preprint hep-th/9912170)
    • (2001) Mod. Phys. Lett. , vol.16 , Issue.22 , pp. 1427-1434
    • Figueroa, H.1    Gracia-Bondía, J.M.2
  • 54
    • 13844280556 scopus 로고    scopus 로고
    • The uses of Connes and Kreimer's algebraic formulation of renormalization theory
    • Figueroa H and Gracia-Bondía J M 2004 The uses of Connes and Kreimer's algebraic formulation of renormalization theory Int. J. Mod. Phys. A 19 2739-54 (Preprint hep-th/0301015)
    • (2004) Int. J. Mod. Phys. , vol.19 , Issue.16 , pp. 2739-2754
    • Figueroa, H.1    Gracia-Bondía, J.M.2
  • 55
    • 24344472627 scopus 로고    scopus 로고
    • Combinatorial Hopf algebras in quantum field theory i
    • Figueroa H and Gracia-Bondía J M 2005 Combinatorial Hopf algebras in quantum field theory I Rev. Math. Phys. 17 881-976 (Preprint hep-th/0408145)
    • (2005) Rev. Math. Phys. , vol.17 , Issue.8 , pp. 881-976
    • Figueroa, H.1    Gracia-Bondía, J.M.2
  • 56
    • 0036174722 scopus 로고    scopus 로고
    • Les algèbres de Hopf des arbres enracinés décorés I, II
    • Foissy L 2002 Les algèbres de Hopf des arbres enracinés décorés I, II Bull. Sci. Math. 126 193-239
    • (2002) Bull. Sci. Math. , vol.126 , Issue.3 , pp. 193-239
    • Foissy, L.1
  • 58
    • 0035961393 scopus 로고    scopus 로고
    • Wave-function renormalization and the Hopf algebra of Connes and Kreimer
    • Girelli F, Krajewski T and Martinetti P 2001 Wave-function renormalization and the Hopf algebra of Connes and Kreimer Mod. Phys. Lett. A 16 299-303 (Preprint math-ph/0103020)
    • (2001) Mod. Phys. Lett. , vol.16 , pp. 299-303
    • Girelli, F.1    Krajewski, T.2    Martinetti, P.3
  • 59
    • 13644251926 scopus 로고    scopus 로고
    • An algebraic Birkhoff decomposition for the continous renormalization group
    • Girelli F, Krajewski T and Martinetti P 2004 An algebraic Birkhoff decomposition for the continous renormalization group J. Math. Phys. 45 4679-97 (Preprint hep-th/0401157)
    • (2004) J. Math. Phys. , vol.45 , Issue.12 , pp. 4679-4697
    • Girelli, F.1    Krajewski, T.2    Martinetti, P.3
  • 60
    • 38249025073 scopus 로고
    • Hopf-algebraic structure of families of trees
    • Grossman R and Larson R G 1989 Hopf-algebraic structure of families of trees J. Algebra 126 184-210
    • (1989) J. Algebra , vol.126 , Issue.1 , pp. 184-210
    • Grossman, R.1    Larson, R.G.2
  • 61
    • 0034147167 scopus 로고    scopus 로고
    • Baxter algebras and shuffle products
    • Guo L and Keigher W 2000 Baxter algebras and shuffle products Adv. Math. 150 117-49 (Preprint math.RA/0407155)
    • (2000) Adv. Math. , vol.150 , Issue.1 , pp. 117-149
    • Guo, L.1    Keigher, W.2
  • 62
    • 0242270113 scopus 로고    scopus 로고
    • Baxter algebras and differential algebras
    • Guo L 2002 Baxter algebras and differential algebras (Differential Algebra and Related Topics (Newark, NJ, 2000) (River Edge, NJ: World Scientific) pp 281-305 (Preprint math.RA/0407180)
    • (2002) (Differential Algebra and Related Topics , pp. 281-305
    • Guo, L.1
  • 63
    • 28844455195 scopus 로고    scopus 로고
    • Baxter algebras, stirling numbers, and partitions
    • Guo L 2005 Baxter algebras, stirling numbers, and partitions J. Algebra Appl. 4 153-64 (Preprint math.AC/0402348)
    • (2005) J. Algebra Appl. , vol.4 , Issue.2 , pp. 153-164
    • Guo, L.1
  • 66
    • 0041862792 scopus 로고    scopus 로고
    • Combinatorics of rooted trees and Hopf algebras
    • Hoffman M 2003 Combinatorics of rooted trees and Hopf algebras Trans. Am. Math. Soc. 355 3795-811 (Preprint math.CO/0201253)
    • (2003) Trans. Am. Math. Soc. , vol.355 , Issue.9 , pp. 3795-3811
    • Hoffman, M.1
  • 67
    • 0038238179 scopus 로고    scopus 로고
    • Comparison of Hopf algebras on trees
    • Holtkamp R 2003 Comparison of Hopf algebras on trees Arch. Math. (Basel) 80 368-83
    • (2003) Arch. Math. (Basel) , vol.80 , pp. 368-383
    • Holtkamp, R.1
  • 68
    • 0002738602 scopus 로고
    • Coalgebras and bialgebras in combinatorics
    • Joni S A and Rota G-C 1979 Coalgebras and bialgebras in combinatorics Stud. Appl. Math. 61 93-139
    • (1979) Stud. Appl. Math. , vol.61 , pp. 93-139
    • Joni, S.A.1    Rota, G.-C.2
  • 71
    • 13644258141 scopus 로고    scopus 로고
    • Connes-Moscovici-Kreimer Hopf Algebras
    • Kastler D 2001 Connes-Moscovici-Kreimer Hopf Algebras Proc. Conf. on 'Mathematical Physics and in Mathematics and Physics' (Siena, 20-25 June 2000) (Providence, RI: American Mathematical Society) Fields Inst. Commun. 30 219-48 (Preprint hep-th/0104017)
    • (2001) Fields Inst. Commun. , vol.30 , pp. 219-248
    • Kastler, D.1
  • 72
    • 84962994320 scopus 로고
    • Spitzer's identity and its use in probability theory
    • Kingman J F C 1962 Spitzer's identity and its use in probability theory J. Lond. Math. Soc. 37 309-16
    • (1962) J. Lond. Math. Soc. , vol.37 , pp. 309-316
    • Kingman, J.F.C.1
  • 73
    • 0039182136 scopus 로고    scopus 로고
    • On Kreimer's Hopf algebra structure of Feynman graphs
    • Krajewski T and Wulkenhaar R 1998 On Kreimer's Hopf algebra structure of Feynman graphs Eur. Phys. J. C 7 697-708 (Preprint hep-th/9805098)
    • (1998) Eur. Phys. J. , vol.7 , Issue.4 , pp. 697-708
    • Krajewski, T.1    Wulkenhaar, R.2
  • 74
    • 33646035766 scopus 로고    scopus 로고
    • On the Hopf algebra structure of perturbative quantum field theories
    • Kreimer D 1998 On the Hopf algebra structure of perturbative quantum field theories Adv. Theor. Math. Phys. 2 303-34 (Preprint q-alg/9707029)
    • (1998) Adv. Theor. Math. Phys. , vol.2 , pp. 303-334
    • Kreimer, D.1
  • 75
    • 33748744827 scopus 로고    scopus 로고
    • Chen's iterated integral represents the operator product expansion
    • Kreimer D 1999 Chen's iterated integral represents the operator product expansion Adv. Theor. Math. Phys. 3 627-670 (Preprint hep-th/9901099)
    • (1999) Adv. Theor. Math. Phys. , vol.3 , pp. 627-670
    • Kreimer, D.1
  • 76
    • 85036702302 scopus 로고    scopus 로고
    • Factorization in quantum field theory: An exercise in Hopf algebras and local singularities contributed to
    • Kreimer D 2003 Factorization in quantum field theory: an exercise in Hopf algebras and local singularities contributed to Les Houches School of Physics: Frontiers in Number Theory, Physics and Geometry (Les Houches, France, 9-21 March) (Preprint hep-th/0306020)
    • (2003) Les Houches School of Physics: Frontiers in Number Theory, Physics and Geometry
    • Kreimer, D.1
  • 77
    • 0000670736 scopus 로고    scopus 로고
    • Shuffling quantum field theory
    • Kreimer D 2000 Shuffling quantum field theory Lett. Math. Phys. 51 179-91 (Preprint hep-th/9912290)
    • (2000) Lett. Math. Phys. , vol.51 , Issue.3 , pp. 179-191
    • Kreimer, D.1
  • 78
    • 0036239309 scopus 로고    scopus 로고
    • Combinatorics of (perturbative) quantum field theory
    • Kreimer D 2002 Combinatorics of (perturbative) quantum field theory Phys. Rep. 363 387-424 (Preprint hep-th/00110059)
    • (2002) Phys. Rep. , vol.363 , Issue.4-6 , pp. 387-424
    • Kreimer, D.1
  • 79
    • 0033426909 scopus 로고    scopus 로고
    • On overlapping divergencies
    • Kreimer D 1999 On overlapping divergencies Commun. Math. Phys. 204 669-89 (Preprint hep-th/9810022)
    • (1999) Commun. Math. Phys. , vol.204 , Issue.3 , pp. 669-689
    • Kreimer, D.1
  • 80
    • 28844476930 scopus 로고    scopus 로고
    • What is the trouble with Dyson-Schwinger equations? contributed to
    • Kreimer D 2004 What is the trouble with Dyson-Schwinger equations? contributed to Proc. Loops and Legs (Zinnowitz, Germany) (Preprint hep-th/0407016)
    • (2004) Proc. Loops and Legs
    • Kreimer, D.1
  • 81
    • 28844465971 scopus 로고    scopus 로고
    • The Residues of Quantum Field Theory-Numbers we should know contributed to
    • Kreimer D 2003 The Residues of Quantum Field Theory-Numbers we should know contributed to Proc. Workshop on Noncommutative Geometry and Number Theory (Max Planck Institut für Mathematik, Bonn, 18-22 Aug.) (Preprint hep-th/0407016)
    • (2003) Proc. Workshop on Noncommutative Geometry and Number Theory
    • Kreimer, D.1
  • 83
    • 0037265094 scopus 로고    scopus 로고
    • New mathematical structures in renormalizable quantum field theory
    • Kreimer D 2003 New mathematical structures in renormalizable quantum field theory Ann. Phys. 303 179-202
    • (2003) Ann. Phys. , vol.303 , Issue.1 , pp. 179-202
    • Kreimer, D.1
  • 84
    • 28844453105 scopus 로고    scopus 로고
    • Structures in Feynman graphs: Hopf algebras and symmetries
    • Kreimer D 2001 Structures in Feynman graphs: Hopf algebras and symmetries Dennisfest Proc. (Stony Brook, June) (Preprint hep-th/0202110)
    • (2001) Dennisfest Proc.
    • Kreimer, D.1
  • 85
    • 18144402422 scopus 로고    scopus 로고
    • Using the Hopf algebra structure of QFT in calculations
    • Kreimer D and Delbourgo R 1999 Using the Hopf algebra structure of QFT in calculations Phys. Rev. D 60 105025 (Preprint hep-th/9903249)
    • (1999) Phys. Rev. , vol.60 , Issue.10 , pp. 105025
    • Kreimer, D.1    Delbourgo, R.2
  • 87
    • 0002939037 scopus 로고    scopus 로고
    • Dialgebras
    • Loday J-L 2001 Dialgebras Dialgebras and Related Operads (Springer Lecture Notes in Mathematics) vol 1763 pp 7-66 (Preprint math.QA/0102053)
    • (2001) Dialgebras and Related Operads , vol.1763 , pp. 7-66
    • Loday, J.-L.1
  • 88
    • 0001230920 scopus 로고    scopus 로고
    • Hopf algebra of the planar binary trees
    • Loday J-L and Ronco M O 1998 Hopf algebra of the planar binary trees Adv. Math. 139 293-309
    • (1998) Adv. Math. , vol.139 , Issue.2 , pp. 293-309
    • Loday, J.-L.1    Ronco, M.O.2
  • 89
    • 24644503776 scopus 로고    scopus 로고
    • Hopf algebra of ribbon graphs and renormalization
    • Malyshev D 2002 Hopf algebra of ribbon graphs and renormalization J. High Energy Phys. 13 28
    • (2002) J. High Energy Phys. , vol.13 , pp. 28
    • Malyshev, D.1
  • 90
    • 18844479535 scopus 로고    scopus 로고
    • 4 theory
    • 4 theory Phys. Lett. B 578 231-4
    • (2004) Phys. Lett. , vol.578 , Issue.1-2 , pp. 231-234
    • Malyshev, D.1
  • 91
    • 9944236447 scopus 로고    scopus 로고
    • Hopf algebras, from basics to applications to renormalization
    • Manchon D 2001 Hopf algebras, from basics to applications to renormalization Comptes-rendus Rencontres math. Glanon (Preprint math.QA/0408405)
    • (2001) Comptes-rendus Rencontres Math. Glanon
    • Manchon, D.1
  • 93
    • 3943081339 scopus 로고    scopus 로고
    • Insertion and elimination lie algebra: The ladder case
    • Mencattini I and Kreimer D 2004 Insertion and elimination lie algebra: the ladder case Lett. Math. Phys. 67 61-74 (Preprint math.QA/0308042)
    • (2004) Lett. Math. Phys. , vol.67 , Issue.1 , pp. 61-74
    • Mencattini, I.1    Kreimer, D.2
  • 94
    • 24144498478 scopus 로고    scopus 로고
    • The structure of the ladder insertion-elimination Lie algebra
    • Mencattini I and Kreimer D 2005 The structure of the ladder insertion-elimination Lie algebra Commun. Math. Phys. 259 413-32 (Preprint mat-th/0408053)
    • (2005) Commun. Math. Phys. , vol.259 , Issue.2 , pp. 413-432
    • Mencattini, I.1    Kreimer, D.2
  • 95
    • 0000859132 scopus 로고
    • On the structure of hopf algebras
    • Milnor J W and Moore J C 1965 On the structure of hopf algebras Ann. Math. 81 211-64
    • (1965) Ann. Math. , vol.81 , pp. 211-264
    • Milnor, J.W.1    Moore, J.C.2
  • 96
    • 0035981787 scopus 로고    scopus 로고
    • Nested sums, expansion of transcendental functions and multiple-loop integrals
    • Moch S, Uwer P and Weinzierl S 2002 Nested sums, expansion of transcendental functions and multiple-loop integrals J. Math. Phys. 43 3363-86 (Preprint hep-ph/0110083)
    • (2002) J. Math. Phys. , vol.43 , Issue.6 , pp. 3363-3386
    • Moch, S.1    Uwer, P.2    Weinzierl, S.3
  • 97
    • 0039334812 scopus 로고    scopus 로고
    • Relating the Connes-Kreimer and Grossmann-Larson Hopf algebras built on rooted trees
    • Panaite F 2000 Relating the Connes-Kreimer and Grossmann-Larson Hopf algebras built on rooted trees Lett. Math. Phys. 51 211-9
    • (2000) Lett. Math. Phys. , vol.51 , Issue.3 , pp. 211-219
    • Panaite, F.1
  • 98
    • 0010326045 scopus 로고    scopus 로고
    • The Hopf algebra structure of Connes and Kreimer in Epstein-Glaser renormalization
    • Pinter G 2000 The Hopf algebra structure of Connes and Kreimer in Epstein-Glaser renormalization Lett. Math. Phys. 54 227-33
    • (2000) Lett. Math. Phys. , vol.54 , Issue.3 , pp. 227-233
    • Pinter, G.1
  • 99
    • 4043101126 scopus 로고    scopus 로고
    • Hopf algebra of renormalization, normal coordinates and Kontsevich deformation quantization
    • Rosenbaum M and Vergara J D 2004 Hopf algebra of renormalization, normal coordinates and Kontsevich deformation quantization J. Phys. A: Math. Gen. 37 7939-53 (Preprint hep-th/0404233)
    • (2004) J. Phys. A: Math. Gen. , vol.37 , Issue.32 , pp. 7939-7953
    • Rosenbaum, M.1    Vergara, J.D.2
  • 100
    • 0010145256 scopus 로고
    • Fluctuation theory and baxter algebras
    • Rota G-C and Smith D 1972 Fluctuation theory and baxter algebras Ist. Naz. Alta Mat. 9 179-201
    • (1972) Ist. Naz. Alta Mat. , vol.9 , pp. 179-201
    • Rota, G.-C.1    Smith, D.2
  • 102
    • 0000087787 scopus 로고
    • Baxter algebras and combinatorial identities. I, II
    • Rota G-C 1969 Baxter algebras and combinatorial identities. I, II Bull. Am. Math. Soc. 75 325-9
    • (1969) Bull. Am. Math. Soc. , vol.75 , pp. 325-329
    • Rota, G.-C.1
  • 105
    • 0002812411 scopus 로고    scopus 로고
    • Ten mathematics problems i will never solve
    • Rota G-C 1998 Ten mathematics problems I will never solve Mitt. Dtsch. Math. -Ver. 2 45-52
    • (1998) Mitt. Dtsch. Math. -Ver. , vol.2 , pp. 45-52
    • Rota, G.-C.1
  • 109
    • 3042595720 scopus 로고    scopus 로고
    • On the differential equations of the characters for the renormalization group
    • Sakakibara M 2004 On the differential equations of the characters for the renormalization group Mod. Phys. Lett. A 19 1453-6 (Preprint math-ph/0401048)
    • (2004) Mod. Phys. Lett. , vol.19 , Issue.19 , pp. 1453-1456
    • Sakakibara, M.1
  • 110
    • 0001706876 scopus 로고
    • Incidence Hopf algebras
    • Schmitt W 1994 Incidence Hopf algebras J. Pure Appl. Algebra 96 299-330
    • (1994) J. Pure Appl. Algebra , vol.96 , Issue.3 , pp. 299-330
    • Schmitt, W.1
  • 112
    • 84967710276 scopus 로고
    • A combinatorial lemma and its application to probability theory
    • Spitzer F 1956 A combinatorial lemma and its application to probability theory Trans. Am. Math. Soc. 82 323-39
    • (1956) Trans. Am. Math. Soc. , vol.82 , pp. 323-339
    • Spitzer, F.1
  • 115
    • 14644443621 scopus 로고    scopus 로고
    • Loops on surfaces, Feynman diagrams, and trees
    • Turaev V 2005 Loops on surfaces, Feynman diagrams, and trees J. Geom. Phys. 53 461-82 (Preprint hep-th/0403266)
    • (2005) J. Geom. Phys. , vol.53 , Issue.4 , pp. 461-482
    • Turaev, V.1
  • 118
    • 28844481255 scopus 로고
    • Orientation
    • Wightman A S 1976 Orientation Renormalization Theory ed G Velo, A S Wightman and D Reidel Proc. of the Int. School of Math. Phys. "Ettore Majorana" (Erice, Italy, 1975) (Dordrecht:) pp 1-24
    • (1976) Renormalization Theory
    • Wightman, A.S.1
  • 119
    • 0001447372 scopus 로고
    • Convergence of Bogoliubov's method of renormalization in momentum space
    • Zimmermann W 1969 Convergence of Bogoliubov's method of renormalization in momentum space Commun. Math. Phys. 15 208-34
    • (1969) Commun. Math. Phys. , vol.15 , Issue.3 , pp. 208-234
    • Zimmermann, W.1


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