A Quantum Field Theoretical Representation of Euler-Zagier Sums

Details A Quantum Field Theoretical Representation of Euler-Zagier Sums A Quantum Field Theoretical Representation of Euler-Zagier Sums

1999-08-13

arxiv.org/abs/math/9908067v3

Int.J.Math.Math.Sci. 31 (2002) 127-148

Mathematics

Quantum Algebra

Standard latex, 31 pages, 13 figures, final published version

Scientific paper

We establish a novel representation of arbitrary Euler-Zagier sums in terms of weighted vacuum graphs. This representation uses a toy quantum field theory with infinitely many propagators and interaction vertices. The propagators involve Bernoulli polynomials and Clausen functions to arbitrary orders. The Feynman integrals of this model can be decomposed in terms of an algebra of elementary vertex integrals whose structure we investigate. We derive a large class of relations between multiple zeta values, of arbitrary lengths and weights, using only a certain set of graphical manipulations on Feynman diagrams. Further uses and possible generalizations of the model are pointed out.

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