메뉴 건너뛰기




Volumn 290, Issue 1, 2009, Pages 291-319

The structure of renormalization Hopf algebras for gauge theories I: Representing Feynman graphs on BV-algebras

Author keywords

[No Author keywords available]

Indexed keywords


EID: 70349673819     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-009-0829-x     Document Type: Article
Times cited : (28)

References (45)
  • 1
    • 21844525170 scopus 로고
    • Removal of divergences with the Batalin-Vilkovisky formalism
    • Anselmi D.: Removal of divergences with the Batalin-Vilkovisky formalism. Class. Quant. Grav. 11, 2181-2204 (1994).
    • (1994) Class. Quant. Grav. , vol.11 , pp. 2181-2204
    • Anselmi, D.1
  • 2
    • 59849099044 scopus 로고    scopus 로고
    • The QED beta-function from global solutions to Dyson-Schwinger equations
    • van Baalen G., Kreimer D., Uminsky D., Yeats K.: The QED beta-function from global solutions to Dyson-Schwinger equations. Ann. Phys. 324, 205-219 (2009).
    • (2009) Ann. Phys. , vol.324 , pp. 205-219
    • van Baalen, G.1    Kreimer, D.2    Uminsky, D.3    Yeats, K.4
  • 3
    • 34249761314 scopus 로고
    • Local BRST cohomology in the antifield formalism. I. General theorems
    • Barnich G., Brandt F., Henneaux M.: Local BRST cohomology in the antifield formalism. I. General theorems. Commun. Math. Phys. 174, 57-92 (1995).
    • (1995) Commun. Math. Phys. , vol.174 , pp. 57-92
    • Barnich, G.1    Brandt, F.2    Henneaux, M.3
  • 4
    • 34249762220 scopus 로고
    • Local BRST cohomology in the antifield formalism. II. Application to Yang-Mills theory
    • Barnich G., Brandt F., Henneaux M.: Local BRST cohomology in the antifield formalism. II. Application to Yang-Mills theory. Commun. Math. Phys. 174, 93-116 (1995).
    • (1995) Commun. Math. Phys. , vol.174 , pp. 93-116
    • Barnich, G.1    Brandt, F.2    Henneaux, M.3
  • 5
    • 33744741883 scopus 로고
    • Gauge algebra and quantization
    • Batalin I.A., Vilkovisky G.A.: Gauge algebra and quantization. Phys. Lett. B102, 27-31 (1981).
    • (1981) Phys. Lett. , vol.B102 , pp. 27-31
    • Batalin, I.A.1    Vilkovisky, G.A.2
  • 6
    • 24844468969 scopus 로고
    • Feynman rules for reducible gauge theories
    • Batalin I.A., Vilkovisky G.A.: Feynman rules for reducible gauge theories. Phys. Lett. B120, 166-170 (1983).
    • (1983) Phys. Lett. , vol.B120 , pp. 166-170
    • Batalin, I.A.1    Vilkovisky, G.A.2
  • 7
    • 30244485015 scopus 로고
    • Quantization of Gauge theories with linearly dependent generators
    • Batalin I.A., Vilkovisky G.A.: Quantization of Gauge theories with linearly dependent generators. Phys. Rev. D28, 2567-2582 (1983).
    • (1983) Phys. Rev. , vol.D28 , pp. 2567-2582
    • Batalin, I.A.1    Vilkovisky, G.A.2
  • 8
    • 33750411572 scopus 로고
    • The abelian Higgs-Kibble model. Unitarity of the S operator
    • Becchi C., Rouet A., Stora R.: The abelian Higgs-Kibble model. Unitarity of the S operator. Phys. Lett. B52, 344 (1974).
    • (1974) Phys. Lett. , vol.B52 , pp. 344
    • Becchi, C.1    Rouet, A.2    Stora, R.3
  • 9
    • 0039454412 scopus 로고
    • Renormalization of the abelian Higgs-Kibble model
    • Becchi C., Rouet A., Stora R.: Renormalization of the abelian Higgs-Kibble model. Commun. Math. Phys. 42, 127-162 (1975).
    • (1975) Commun. Math. Phys. , vol.42 , pp. 127-162
    • Becchi, C.1    Rouet, A.2    Stora, R.3
  • 10
    • 0542393957 scopus 로고
    • Renormalization of gauge theories
    • Becchi C., Rouet A., Stora R.: Renormalization of gauge theories. Annals Phys. 98, 287-321 (1976).
    • (1976) Annals Phys. , vol.98 , pp. 287-321
    • Becchi, C.1    Rouet, A.2    Stora, R.3
  • 11
    • 18244405039 scopus 로고    scopus 로고
    • The Hopf algebra of rooted trees in Epstein-Glaser renormalization
    • Bergbauer C., Kreimer D.: The Hopf algebra of rooted trees in Epstein-Glaser renormalization. Ann. H. Poincaré 6, 343-367 (2005).
    • (2005) Ann. H. Poincaré , vol.6 , pp. 343-367
    • Bergbauer, C.1    Kreimer, D.2
  • 12
    • 35348877778 scopus 로고    scopus 로고
    • Hopf algebras in renormalization theory: Locality and Dyson-Schwinger equations from Hochschild cohomology
    • Bergbauer C., Kreimer D.: Hopf algebras in renormalization theory: Locality and Dyson-Schwinger equations from Hochschild cohomology. IRMA Lect. Math. Theor. Phys. 10, 133-164 (2006).
    • (2006) IRMA Lect. Math. Theor. Phys. , vol.10 , pp. 133-164
    • Bergbauer, C.1    Kreimer, D.2
  • 13
    • 67749104008 scopus 로고    scopus 로고
    • Mixed Hodge structures and renormalization in physics
    • Bloch S., Kreimer D.: Mixed Hodge structures and renormalization in physics. Commun. Num. Theor. Phys. 2 4, 637-718 (2008).
    • (2008) Commun. Num. Theor. Phys. 2 , vol.4 , pp. 637-718
    • Bloch, S.1    Kreimer, D.2
  • 14
    • 0012574961 scopus 로고    scopus 로고
    • Renormalization of QED with planar binary trees
    • Brouder C., Frabetti A.: Renormalization of QED with planar binary trees. Eur. Phys. J. C19, 715-741 (2001).
    • (2001) Eur. Phys. J. , vol.C19 , pp. 715-741
    • Brouder, C.1    Frabetti, A.2
  • 15
    • 32044436928 scopus 로고    scopus 로고
    • Non-commutative Hopf algebra of formal diffeomorphisms
    • Brouder C., Frabetti A., Krattenthaler C.: Non-commutative Hopf algebra of formal diffeomorphisms. Adv. Math. 200, 479-524 (2006).
    • (2006) Adv. Math. , vol.200 , pp. 479-524
    • Brouder, C.1    Frabetti, A.2    Krattenthaler, C.3
  • 16
    • 0034348733 scopus 로고    scopus 로고
    • Microlocal analysis and interacting quantum field theories: Renormalization on physical backgrounds
    • Brunetti R., Fredenhagen K.: Microlocal analysis and interacting quantum field theories: Renormalization on physical backgrounds. Commun. Math. Phys. 208, 623-661 (2000).
    • (2000) Commun. Math. Phys. , vol.208 , pp. 623-661
    • Brunetti, R.1    Fredenhagen, K.2
  • 17
    • 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., Kreimer D.: 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, 249-273 (2000).
    • (2000) Commun. Math. Phys. , vol.210 , pp. 249-273
    • Connes, A.1    Kreimer, D.2
  • 18
    • 0035530562 scopus 로고    scopus 로고
    • Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The beta-function, diffeomorphisms and the renormalization group
    • Connes A., Kreimer D.: Renormalization in quantum field theory and the Riemann-Hilbert problem. II: The beta-function, diffeomorphisms and the renormalization group. Commun. Math. Phys. 216, 215-241 (2001).
    • (2001) Commun. Math. Phys. , vol.216 , pp. 215-241
    • Connes, A.1    Kreimer, D.2
  • 19
    • 70349702977 scopus 로고    scopus 로고
    • Dütsch, M., Fredenhagen, K.: Perturbative algebraic field theory, and deformation quantization. In: Mathematical physics in mathematics and physics (Siena, 2000), Volume 30 of Fields Inst. Commun., Providence, RI: Amer. Math. Soc., 2001, pp. 151-160
    • Dütsch, M., Fredenhagen, K.: Perturbative algebraic field theory, and deformation quantization. In: Mathematical physics in mathematics and physics (Siena, 2000), Volume 30 of Fields Inst. Commun., Providence, RI: Amer. Math. Soc., 2001, pp. 151-160.
  • 21
    • 40849136305 scopus 로고    scopus 로고
    • Faà di Bruno subalgebras of the Hopf algebra of planar trees from combinatorial Dyson- Schwinger equations
    • Foissy L.: Faà di Bruno subalgebras of the Hopf algebra of planar trees from combinatorial Dyson- Schwinger equations. Adv. Math. 218, 136-162 (2008).
    • (2008) Adv. Math. , vol.218 , pp. 136-162
    • Foissy, L.1
  • 22
    • 36149023949 scopus 로고
    • Quantum electrodynamics at small distances
    • Gell-Mann M., Low F.E.: Quantum electrodynamics at small distances. Phys. Rev. 95, 1300-1312 (1954).
    • (1954) Phys. Rev. , vol.95 , pp. 1300-1312
    • Gell-Mann, M.1    Low, F.E.2
  • 23
    • 0001523110 scopus 로고
    • The cohomology structure of an associative ring
    • Gerstenhaber M.: The cohomology structure of an associative ring. Ann. of Math. 78, 267-288 (1963).
    • (1963) Ann. of Math. , vol.78 , pp. 267-288
    • Gerstenhaber, M.1
  • 24
    • 0035961393 scopus 로고    scopus 로고
    • Wave-function renormalization and the Hopf algebra of Connes and Kreimer
    • Girelli F., Krajewski T., Martinetti P.: Wave-function renormalization and the Hopf algebra of Connes and Kreimer. Mod. Phys. Lett. A16, 299-303 (2001).
    • (2001) Mod. Phys. Lett. , vol.A16 , pp. 299-303
    • Girelli, F.1    Krajewski, T.2    Martinetti, P.3
  • 25
    • 13644251926 scopus 로고    scopus 로고
    • An algebraic Birkhoff decomposition for the continuous renormalization group
    • Girelli F., Krajewski T., Martinetti P.: An algebraic Birkhoff decomposition for the continuous renormalization group. J. Math. Phys. 45, 4679-4697 (2004).
    • (2004) J. Math. Phys. , vol.45 , pp. 4679-4697
    • Girelli, F.1    Krajewski, T.2    Martinetti, P.3
  • 26
    • 0030591387 scopus 로고    scopus 로고
    • Are nonrenormalizable gauge theories renormalizable?
    • Gomis J., Weinberg S.: Are nonrenormalizable gauge theories renormalizable?. Nucl. Phys. B469, 473-487 (1996).
    • (1996) Nucl. Phys. , vol.B469 , pp. 473-487
    • Gomis, J.1    Weinberg, S.2
  • 27
    • 70349698275 scopus 로고    scopus 로고
    • Hartshorne, R.: Algebraic Geometry. Number 52 in Graduate Texts in Mathematics. New York: Springer-Verlag, 1977
    • Hartshorne, R.: Algebraic Geometry. Number 52 in Graduate Texts in Mathematics. New York: Springer-Verlag, 1977.
  • 28
    • 52949110626 scopus 로고    scopus 로고
    • Renormalized quantum Yang-Mills fields in curved spacetime
    • Hollands S.: Renormalized quantum Yang-Mills fields in curved spacetime. Rev. Math. Phys. 20, 1033-1172 (2008).
    • (2008) Rev. Math. Phys. , vol.20 , pp. 1033-1172
    • Hollands, S.1
  • 29
    • 0038648979 scopus 로고    scopus 로고
    • On the renormalization group in curved spacetime
    • Hollands S., Wald R.M.: On the renormalization group in curved spacetime. Commun. Math. Phys. 237, 123-160 (2003).
    • (2003) Commun. Math. Phys. , vol.237 , pp. 123-160
    • Hollands, S.1    Wald, R.M.2
  • 30
    • 70349701494 scopus 로고    scopus 로고
    • Wilsonian renormalization, differential equations and Hopf algebras
    • Krajewski, T., Martinetti P.: Wilsonian renormalization, differential equations and Hopf algebras. http://arXiv.org/abs/:0806.4309v2[hepth], 2008.
    • (2008)
    • Krajewski, T.1    Martinetti, P.2
  • 31
    • 33646035766 scopus 로고    scopus 로고
    • On the Hopf algebra structure of perturbative quantum field theories
    • Kreimer D.: On the Hopf algebra structure of perturbative quantum field theories. Adv. Theor. Math. Phys. 2, 303-334 (1998).
    • (1998) Adv. Theor. Math. Phys. , vol.2 , pp. 303-334
    • Kreimer, D.1
  • 32
    • 33748058596 scopus 로고    scopus 로고
    • Anatomy of a gauge theory
    • Kreimer D.: Anatomy of a gauge theory. Ann. Phys. 321, 2757-2781 (2006).
    • (2006) Ann. Phys. , vol.321 , pp. 2757-2781
    • Kreimer, D.1
  • 33
    • 37349024000 scopus 로고    scopus 로고
    • A remark on quantum gravity
    • Kreimer D.: A remark on quantum gravity. Ann. Phys. 323, 49-60 (2008).
    • (2008) Ann. Phys. , vol.323 , pp. 49-60
    • Kreimer, D.1
  • 34
    • 70349699960 scopus 로고    scopus 로고
    • Not so non-renormalizable gravity
    • Kreimer, D.: Not so non-renormalizable gravity. http://arXiv.org/abs/0805.4545v1[hepth], 2008.
    • (2008)
    • Kreimer, D.1
  • 35
    • 70349701495 scopus 로고    scopus 로고
    • Kreimer, D., van Suijlekom, W.D.: Work in progress
    • Kreimer, D., van Suijlekom, W.D.: Work in progress.
  • 36
    • 33749460339 scopus 로고    scopus 로고
    • An étude in non-linear Dyson-Schwinger equations
    • Kreimer D., Yeats K.: An étude in non-linear Dyson-Schwinger equations. Nucl. Phys. B Proc. Suppl. 160, 116-121 (2006).
    • (2006) Nucl. Phys. B Proc. Suppl. , vol.160 , pp. 116-121
    • Kreimer, D.1    Yeats, K.2
  • 37
    • 0010326045 scopus 로고    scopus 로고
    • The Hopf algebra structure of Connes and Kreimer in Epstein-Glaser renormalization
    • Pinter G.: The Hopf algebra structure of Connes and Kreimer in Epstein-Glaser renormalization. Lett. Math. Phys. 54, 227-233 (2000).
    • (2000) Lett. Math. Phys. , vol.54 , pp. 227-233
    • Pinter, G.1
  • 38
    • 70349715336 scopus 로고    scopus 로고
    • Saunders, D.J.: The Geometry of Jet Bundles. Cambridge: Cambridge University Press, 1989
    • Saunders, D.J.: The Geometry of Jet Bundles. Cambridge: Cambridge University Press, 1989.
  • 39
    • 70349721608 scopus 로고    scopus 로고
    • Stasheff, J.: Deformation theory and the Batalin-Vilkovisky master equation. In: Deformation theory and symplectic geometry (Ascona, 1996), Volume 20 of Math. Phys. Stud., Dordrecht: Kluwer Acad. Publ., 1997, pp. 271-284
    • Stasheff, J.: Deformation theory and the Batalin-Vilkovisky master equation. In: Deformation theory and symplectic geometry (Ascona, 1996), Volume 20 of Math. Phys. Stud., Dordrecht: Kluwer Acad. Publ., 1997, pp. 271-284.
  • 40
    • 35548932467 scopus 로고    scopus 로고
    • Renormalization of gauge fields: A Hopf algebra approach
    • van Suijlekom W.D.: Renormalization of gauge fields: A Hopf algebra approach. Commun. Math. Phys. 276, 773-798 (2007).
    • (2007) Commun. Math. Phys. , vol.276 , pp. 773-798
    • van Suijlekom, W.D.1
  • 41
    • 70349715335 scopus 로고    scopus 로고
    • van Suijlekom, W.D.: Multiplicative renormalization and Hopf algebras. In: Ceyhan, O., Manin, Y.-I., Marcolli, M. eds, Arithmetic and Geometry Around Quantization. Basel: Birkhäuser Verlag, 2008
    • van Suijlekom, W.D.: Multiplicative renormalization and Hopf algebras. In: Ceyhan, O., Manin, Y.-I., Marcolli, M. eds, Arithmetic and Geometry Around Quantization. Basel: Birkhäuser Verlag, 2008.
  • 42
    • 70349724731 scopus 로고    scopus 로고
    • van Suijlekom, W.D.: Renormalization of gauge fields using Hopf algebras. In: Fauser, J.T.B., Zeidler, E., eds., Quantum Field Theory. Basel: Birkhäuser Verlag, 2008
    • van Suijlekom, W.D.: Renormalization of gauge fields using Hopf algebras. In: Fauser, J.T.B., Zeidler, E., eds., Quantum Field Theory. Basel: Birkhäuser Verlag, 2008.
  • 43
    • 0038314799 scopus 로고    scopus 로고
    • Gauge invariance in field theory and statistical physics in operator formalism
    • LEBEDEV-75-39, available at, [hepth]
    • Tyutin, I.V.: Gauge invariance in field theory and statistical physics in operator formalism. LEBEDEV-75-39, available at http://arXiv.org/abs/0812.0580v2[hepth], 2008.
    • (2008)
    • Tyutin, I.V.1
  • 44
    • 70349710812 scopus 로고    scopus 로고
    • Waterhouse, W.C.: Introduction to Affine Group Schemes. New York: Springer, 1979
    • Waterhouse, W.C.: Introduction to Affine Group Schemes. New York: Springer, 1979.
  • 45
    • 0010116847 scopus 로고
    • Renormalization group methods
    • Wilson K.G.: Renormalization group methods. Adv. in Math. 16, 170-186 (1975).
    • (1975) Adv. in Math. , vol.16 , pp. 170-186
    • Wilson, K.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.