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Graphons and renormalization of large Feynman diagrams

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Języki publikacji
EN
Abstrakty
EN
The article builds a new enrichment of the Connes-Kreimer renormalization Hopf algebra of Feynman diagrams in the language of graph functions.
Rocznik
Strony
427--455
Opis fizyczny
Bibliogr. 41 poz.
Twórcy
  • 1461863596 Marzdaran Blvd. Tehran, Iran
Bibliografia
  • [1] C. Bergbauer, D. Kreimer, Hopf algebras in renormalization theory: Locality and Dyson-Schwinger equations from Hochschild cohomology, IRMA Lect. Math. Theor. Phys. 10 (2006), 133-164.
  • [2] B. Bollobas, O. Riordan, Metrics for sparse graphs, Surveys in Combinatorics 2009, 211-287, LMS Lecture Notes Series, vol. 365, Cambridge Univ. Press, Cambridge, 2009.
  • [3] C. Borgs, J.T. Chayes, L. Lovasz, Moments of two-variable functions and the uniqueness of graph limits, Geom. Funct. Anal. 19 (2010) 6, 1597-1619.
  • [4] C. Borgs, J.T. Chayes, L. Lovasz, V.T. Sos, K. Vesztergombi, Convergent sequences of dense graphs I. Subgraph frequencies, metric properties and testing, Adv. Math. 219 (2008) 6, 1801-1851.
  • [5] C. Borgs, J.T. Chayes, L. Lovasz, V.T. Sos, K. Vesztergombi, Convergent sequences of dense graphs II. Multiway cuts and statistical physics, Ann. Math. (2) 176 (2012) 1, 151-219.
  • [6] P. Breitenlohner, D. Maison (eds.), Quantum, Field Theory, Proceedings of the Ringberg Workshop Held at Tegernsee, Germany, 21-24 June 1998, on the Occasion of Wolfhart Zimmermann's 70th Birthday, Springer, 2000.
  • [7] E. Brezin, C. Itzykson, G. Parisi, J.B. Zuber, Planar diagrams, Comm. Math. Phys. 59 (1978) 1, 35-51.
  • [8] D.J. Broadhurst, D. Kreimer, Renormalization automated by Hopf algebra, J. Symb. Comput. 27 (1999) 6, 581-600.
  • [9] C. Brouder, On the trees of quantum fields, Eur. Phys. J. C 12 (2000), 535-549.
  • [10] C. Brouder, A. Frabetti, Renormalization of QED with planar binary trees, Eur. Phys. J. C 19 (2001), 715-741.
  • [11] C. Brouder, A. Frabetti, QED Hopf algebras on planar binary trees, J. Alg. 267 (2003), 298-322.
  • [12] C. Brouder, A. Frabetti, F. Menous, Combinatorial Hopf algebras from renormalization, J. Algebraic Combin. 32 (2010) 4, 557-578.
  • [13] D. Calaque, T. Strobl (eds.), Mathematical Aspects of Quantum Field Theories, Mathematical Physics Studies, Springer, 2015.
  • [14] A. Connes, D. Kreimer, 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 (2000) 1, 249-273.
  • [15] A. Connes, D. Kreimer, Renormalization in quantum field theory and the Riemann-Hilbert problem. 2. The /3-function, diffeomorphisms and the renormalization group, Comm. Math. Phys. 216 (2001) 1, 215-241.
  • [16] P. Diaconis, S. Holmes, S. Janson, Interval graph limits, Ann. Comb. 17 (2013) 1, 27-52.
  • [17] P. Diaconis, S. Janson, Graph limits and exchangeable random graphs, Rend. Mat. Appl. (7)28 (2008) 1, 33-61.
  • [18] L. Foissy, Fad di Bruno subalgebras of the Hopf algebra of planar trees from combinatorial Dyson-Schwinger equations, Adv. Math. 218 (2008) 1, 136-162.
  • [19] L. Foissy, General Dyson-Schwinger equations and systems, Comm. Math. Phys. 327 (2014) 1, 151-179.
  • [20] M.E. Hoffman, Combinatorics of rooted trees and Hopf algebras, Trans. Amer. Math. Soc. 355 (2003) 9, 3795-3811.
  • [21] R. Holtkamp, Comparison of Hopf algebras on trees, Arch. Math. 80 (2003) 4, 368-383.
  • [22] S. Janson, Graphons, cut norm, and distance, couplings and rearrangements, NYJM Monographs, vol. 4, 2013.
  • [23] T. Krajewski, R. Wulkenhaar, On Kreimer's Hopf algebra structure on Feynman graphs, Eur. Phys. J. C 7 (1999) 4, 697-708.
  • [24] D. Kreimer, Structures in Feynman graphs: Hopf algebras and symmetries, Proc. Symp. Pure Math. 73 (2005), 43-78.
  • [25] D. Kreimer, Anatomy of a gauge theory, Ann. Phys. 321 (2006), 27-57.
  • [26] D. Kreimer, Dyson-Schwinger equations: from, Hopf algebras to number theory, [in:] Universality and renormalization, Fields Inst. Commun. 50, Amer. Math. Soc, Providence, RI, 2007, pp. 225-248.
  • [27] L. Lovasz, Large networks and graph limits, American Mathematical Society Colloquium Publications, vol. 60, Amer. Math. Soc, Providence, RI, 2012.
  • [28] L. Lovasz, B. Szegedy, Limits of dense graph sequences, J. Combin. Theory Ser. B 96 (2006) 6, 933-957.
  • [29] I. Moerdijk, On the Connes-Kreimer construction of Hopf algebras, Cont. Math. 271 (2001), 311-321.
  • [30] F. Panaite, Relating the Connes-Kreimer and Grossman-Larson Hopf algebras built on rooted trees, Lett. Math. Phys. 51 (2000) 3, 211-219.
  • [31] V. Parameswaran Nair, Quantum, Field Theory: A Modern Perspective, Graduate Texts in Contemporary Physics, Springer, 2005.
  • [32] F. Paugam, Towards the Mathematics of Quantum Field Theory, Ergebnisse der Mathe-matik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, Springer, vol. 59, 2014.
  • [33] A. Shojaei-Fard, The global /3-functions from, solutions of Dyson-Schwinger equations, Modern Phys. Lett. A 28 (2013) 34, 1350152, 12 pp.
  • [34] A. Shojaei-Fard, Counterterms in the context of the universal Hopf algebra of renormalization, Internat. J. Modern Phys. A 29 (2014) 8, 1450045, 15 pp.
  • [35] A. Shojaei-Fard, A new perspective on intermediate algorithms via the Riemann-Hilbert correspondence, Quantum Stud. Math. Found. 4 (2017) 2, 127-148.
  • [36] A. Shojaei-Fard, A measure theoretic perspective on the space of Feynman diagrams, Bol. Soc. Mat. Mex., DOI: 10.1007/s40590-017-0166-6.
  • [37] A. Tanasa, Overview of the parametric representation of renormalizable noncommutative field theory, J. Phys.: Conf. Ser. 103 (2008), 012012.
  • [38] W.D. van Suijlekom, Renormalization of gauge fields: A Hopf algebra approach, Comm. Math. Phys. 276 (2007) 3, 773-798.
  • [39] S. Weinzierl, Introduction to Feynman integrals, [in:] Geometric and topological methods for quantum field theory, Proceedings of the 2009 Villa de Leyva Summer School, Cambridge Univ. Press, 2013, pp. 144-187.
  • [40] S. Weinzierl, Hopf algebras and Dyson-Schwinger equations, Front. Phys. 11 (2016), 111206.
  • [41] K. Yeats, A Combinatorial Perspective on Quantum Field Theory, Springer Briefs in Mathematical Physics, vol. 15, Springer, 2017.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-165fa21e-d64b-4ad5-b8d4-490121f7cca8
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