• Corpus ID: 17514613

Selberg Integrals, Multiple Zeta Values and Feynman Diagrams

@inproceedings{Wohl2002SelbergIM,
  title={Selberg Integrals, Multiple Zeta Values and Feynman Diagrams},
  author={David H. Wohl},
  year={2002}
}
We prove that there is an isomorphism between the Hopf Algebra of Feynman diagrams and the Hopf algebra corresponding to the Homogenous Multiple Zeta Value ring H in C > . In other words, Feynman diagrams evaluate to Multiple Zeta Values in all cases. This proves a recent conjecture of Connes-Kreimer, and others including Broadhurst and Kontsevich. The key step of our theorem is to present the Selberg integral as discussed in Terasoma [22] as a Functional from the Rooted Trees Operad to the… 

References

SHOWING 1-10 OF 24 REFERENCES
Deformations of algebras over operads and Deligne's conjecture
In present paper we develop the deformation theory of operads and algebras over operads. Free resolutions (constructed via Boardman-Vogt approach) are used in order to describe formal moduli spaces
Lectures on the asymptotic expansion of a Hermitian matrix integral
In these lectures three different methods of computing the asymptotic expansion of a Hermitian matrix integral is presented. The first one is a combinatorial method using Feynman diagrams. This leads
Kontsevich's integral for the Kauffman polynomial
Kontsevich's integral is a knot invariant which contains in itself all knot invariants of finite type, or Vassiliev's invariants. The value of this integral lies in an algebra d0, spanned by chord
A geometric parametrization for the virtual Euler characteristic for the moduli spaces of real and complex algebriac curves
We show that the virtual Euler characteristics of the moduli spaces of $s$-pointed algebraic curves of genus $g$ can be determined from a polynomial in $1/\gamma$ where $\gamma$ permits
Nested sums, expansion of transcendental functions and multiscale multiloop integrals
Expansion of higher transcendental functions in a small parameter are needed in many areas of science. For certain classes of functions this can be achieved by algebraic means. These algebraic tools
Selberg integral and multiple zeta values
In this paper, we show that the coefficient of the Taylor expansion of Selberg integrals with respect to exponent variables are expressed as a linear combination of multiple zeta values. We use
On associators and the Grothendieck-Teichmuller group, I
Abstract. We present a formalism within which the relationship (discovered by Drinfel'd in [Dr1], [Dr2]) between associators (for quasi-triangular quasi-Hopf algebras) and (a variant of) the
...
...