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The residues of quantum field theory - numbers we should know

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Noncommutative Geometry and Number Theory

Part of the book series: Aspects of Mathematics ((ASMA))

Abstract

We discuss in an introductory manner structural similarities between the polylogarithm and Green functions in quantum field theory.

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References

  1. D. Kreimer: Locality, Hochschild cohomology and Dyson-Schwinger equations. In preparation.

    Google Scholar 

  2. S. Bloch: Function Theory of Polylogarithms. In: Structural properties of polylogarithms, 275–285, Math. Surveys Monogr., 37, Amer. Math. Soc., Providence, RI, 1991.

    Google Scholar 

  3. D. Kreimer: New mathematical structures in renormalizable quantum field theories. Annals Phys. 303 (2003) 179 [Erratum-ibid. 305 (2003) 79] [arXiv:hep-th/0211136].

    Article  MATH  MathSciNet  Google Scholar 

  4. D. Kreimer: Factorization in quantum field theory: an exercise in Hopf algebras and local singularities. Preprint IHES/P/03/38, hep-th/0306020.

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  5. A. Connes and D. Kreimer: Hopf algebras, renormalization and non-commutative geometry. Commun. Math. Phys. 199 (1998), 203–242; hep-th/9808042

    Article  MATH  MathSciNet  Google Scholar 

  6. K. Ebrahimi-Fard, D. Kreimer: Integrable Renormalization II: The General Case. IHES/P/04/08, hep-th/0403118.

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  7. D. Kreimer: Chen’s iterated integral represents the operator product expansion. Adv. Theor. Math. Phys. 3 (2000) 3 [Adv. Theor. Math. Phys. 3 (1999) 627] [arXiv:hep-th/9901099].

    MathSciNet  Google Scholar 

  8. R. Delbourgo, D. Kreimer: Using the Hopf algebra structure of QFT in calculations. Phys. Rev. D 60 (1999) 105025 [arXiv:hep-th/9903249].

    Article  MathSciNet  Google Scholar 

  9. C. Bergbauer and D. Kreimer: The Hopf algebra of rooted trees in Epstein-Glaser renormalization. Preprint IHES/P/04/12, hep-th/0403207.

    Google Scholar 

  10. D.J. Broadhurst, D. Kreimer: Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality. Nucl. Phys. B 600 (2001) 403 [arXiv:hepth/0012146].

    Article  MATH  Google Scholar 

  11. R. Delbourgo: Self-consistent nonperturbative anomalous dimensions. J. Phys. A 36 (2003) 11697 [arXiv:hep-th/0309047].

    Article  MATH  MathSciNet  Google Scholar 

  12. A. Connes and D. Kreimer: 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 (2000) 249–273; hep-th/9912092

    Article  MATH  MathSciNet  Google Scholar 

  13. A. Connes and M. Marcolli: From Physics to Number Theory via Noncommutative Geometry I: Quantum Statistical Mechanics of Q-lattices. Preprint math.nt/0404128.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institut des Hautes Études Scientifiques, 35 rte. de Chartres, F-91440, Bures-sur-Yvette

    Dirk Kreimer

  2. Center for Mathematical Physics, Boston University, Boston, MA, 02215

    Dirk Kreimer

Authors
  1. Dirk Kreimer
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Editor information

Editors and Affiliations

  1. Department of Mathematics, The Johns Hopkins University, 3400 North Charles Street, Baltimore, MD, 21218, USA

    Caterina Consani

  2. Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111, Bonn

    Matilde Marcolli

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© 2006 Friedr. Vieweg & Sohn Verlag ∣ GWV Fachverlage GmbH, Wiesbaden

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Kreimer, D. (2006). The residues of quantum field theory - numbers we should know. In: Consani, C., Marcolli, M. (eds) Noncommutative Geometry and Number Theory. Aspects of Mathematics. Vieweg. https://doi.org/10.1007/978-3-8348-0352-8_9

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