A quantum field theoretical representation of Euler-Zagier sums
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 order...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202106028 |
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| Summary: | 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 a
vertex algebra 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
generalisations of the model are pointed out. |
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| ISSN: | 0161-1712 1687-0425 |