This course introduces quantum field theory and in particular renormalization theory from the viewpoint of Hopf algebras. As such, it introduces the student to quantum field theory from a modern mathematical viewpoint. While this is of some interest to mathematicians, it has also implications for our understanding of physics, see
Not non-renormalizable gravity and other feasts
and references there.
The course provides in a self-contained manner the necessary background to understand such developments. Here, we collect some background material for reading.
  • Syllabus An optimistic overview of what could be covered. We came close though in previous years.
  • pQFT
    • Two reviews are:
  • Review (D.Kreimer, Annals Phys.303:179-202,2003)
  • Review (D.Manchon, preprint)
  • Assignment 1
  • Solution 1
  • Assignment 2
    • Solution 2
    Here are some papers which cover the metarial of the course:
  • Paper (D.Kreimer, Adv.Theor.Math.Phys.3:627-670,1999)

    • The paper gives in section 3.1 the proof that S_R is a character.
  • Paper (A.Connes, D.Kreimer, Comm.Math.Phys.199, 203-242, 1998))

    • Sections two and three in particular.
  • Paper (A.Connes, D.Kreimer, Comm.Math.Phys.216, 215, 2001))

    • Sections two and four in particular.
  • Paper (K.Ebrahimi-Fard, L.Guo, D.Kreimer, to appear in Ann.H.Poincar'e)

    • Section three summarizes the algebra of rooted trees nicely.
  • Paper D.Kreimer, to appear in the Les Hoches "From Physics to geometry and Number Theory" Proceedings 2003, see also hep-th/0404090 and hep-th/0407016 and hep-th/0012146 (with Broadhurst).

    • Examples for non-linear DSEs.
     Thesis of Igor Mencattini

    The two reviews above cover the material of the course from the viewpoint of physics and mathematics.
    Here are some notes on the course.
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