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Communications in Mathematical Physics

, Volume 225, Issue 3, pp 465–485 | Cite as

Normal Coordinates and Primitive Elements¶in the Hopf Algebra of Renormalization

  • C. Chryssomalakos
  • H. Quevedo
  • M. Rosenbaum
  • J. D. Vergara

Abstract:

We introduce normal coordinates on the infinite dimensional group G introduced by Connes and Kreimer in their analysis of the Hopf algebra of rooted trees. We study the primitive elements of the algebra and show that they are generated by a simple application of the inverse Poincaré lemma, given a closed left invariant 1-form on G. For the special case of the ladder primitives, we find a second description that relates them to the Hopf algebra of functionals on power series with the usual product. Either approach shows that the ladder primitives are given by the Schur polynomials. The relevance of the lower central series of the dual Lie algebra in the process of renormalization is also discussed, leading to a natural concept of k-primitiveness, which is shown to be equivalent to the one already in the literature.

Keywords

Power Series Hopf Algebra Rooted Tree Simple Application Primitive Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • C. Chryssomalakos
    • 1
  • H. Quevedo
    • 1
  • M. Rosenbaum
    • 1
  • J. D. Vergara
    • 1
  1. 1.Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apdo. Postal 70-543,¶04510 México, D.F., Mexico. E-mail: {chryss,quevedo,mrosen,vergara}@nuclecu.unam.mxMX

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